Scattering correction method and device, digital equipment and computer readable storage medium

Abstract

The invention provides a scatter correction method and device, digital equipment and a computer readable storage medium. The method comprises the following steps: acquiring a downsampling response line based on detection data; based on a late one-step iterative algorithm or an optimization migration iterative algorithm, obtaining an estimation objective function corresponding to each downsampling response line by using a moment estimation method; solving the estimation objective function, and obtaining the number of scattering coincidence events corresponding to each downsampling response line; performing up-sampling processing on the down-sampling response line to obtain an up-sampling response line; and calculating the number of scattering coincidence events corresponding to each up-sampling response line. According to the embodiment of the invention, the method does not depend on the activity image and the attenuation image during scatter correction, does not need to adjust the initial iteration value, can achieve the specific setting according to the needs, is simple in implementation, and is high in accuracy.

Description

Technical Field

[0001] This application relates to the field of signal sampling technology, specifically to a scattering correction method, apparatus, digitization device, and computer-readable storage medium. Background Technology

[0002] Positron emission tomography (PET) works by labeling a compound with a radionuclide that can participate in blood flow or metabolic processes in living tissue. The compound is then injected into the organism. The positrons emitted by the radionuclide combine with electrons in the organism, resulting in electron-electron annihilation and producing two gamma photons of equal energy but opposite directions. Because these two gamma photons travel in different directions, the detector detects them at different times. If two scintillation crystals on the Line of Response (LOR) in the detector detect both gamma photons within a specified coincidence time window (e.g., 0–15 nanoseconds), the event of detecting these two gamma photons is called a coincidence event.

[0003] Coincidence events generally include true coincidence events, scattering coincidence events, and random coincidence events. A true coincidence event occurs when the time difference between the arrival of two gamma photons from the same annihilation event at two scintillation crystals located on the response line falls within the coincidence time window. A random coincidence event is a false coincidence event; in a random coincidence event, two detected gamma photons originate from different annihilation events but are mistakenly identified as occurring "simultaneously" within the coincidence time window. A scattering coincidence event refers to the following: for two gamma photons detected from the same annihilation event, one of the gamma photons changes its flight direction due to physical effects such as Compton scattering and / or Rayleigh scattering during its flight.

[0004] Of these three types of coincidence events, the data acquired for random coincidence events and scattering coincidence events may be erroneous, which could affect the resolution, contrast, and positioning accuracy of PET imaging. Therefore, correcting the acquired coincidence events is crucial.

[0005] Currently, commonly used scattering correction methods mainly include multi-window techniques, convolution / deconvolution techniques, and simulation-based techniques. Among these, simulation-based techniques are the most accurate and widely used.

[0006] Simulation-based techniques generally include single-scattering simulation, two-scattering simulation, and Monte Carlo simulation. Single-scattering simulation, for each response line, selects a scattering point from the input activity and decay images to obtain the photon path of a single scattering (i.e., a pair of gamma photons scatters only once). It calculates the single-scattering events along all photon paths corresponding to that response line. Finally, using tail data containing only scattering events, it fits the obtained single-scattering events using tail fitting (TF) to obtain a stretching factor for the scattering coincidence events, which is then applied to all data to achieve scattering correction. Two-scattering simulation is often used in conjunction with single-scattering simulation. The main difference is that two-scattering simulation uses two scattering points to determine the photon path. Monte Carlo simulation primarily determines the total scattering distribution by simulating the motion of each gamma photon pair determined based on the input activity and decay images.

[0007] In the process of developing this application, the inventors discovered that simulation-based technologies have at least the following problems:

[0008] (1) Single scattering simulation methods only consider the case of single scattering. However, in reality, multiple scattering may occur, which may lead to lower accuracy of scattering correction results and thus lower quality of reconstructed images. Although double scattering simulation methods and Monte Carlo simulation methods consider the case of multiple scattering, the calculation process is complex and computationally intensive, which slows down the image reconstruction process and is inefficient.

[0009] (2) Scattering events need to be determined before reconstructing the activity image. However, simulation-based methods for determining scattering events require prior knowledge of the activity image, and existing technologies make it difficult to obtain accurate activity images.

[0010] (3) Since it is difficult to obtain activity images outside the field of view, existing technologies usually do not take into account external radiation (i.e., scattering events generated by gamma photon pairs located outside the field of view), which may lead to lower accuracy of the correction results and thus affect the quality of the reconstructed image.

[0011] (4) Currently, the moment estimation method is used to obtain the estimated objective function corresponding to each downsampled response line. The estimated objective function assumes that the probability density functions of unscattered photons and scattered photons are the same, which leads to the inaccuracy of the number of scattering coincidence events corresponding to the downsampled response line. In view of this, there is an urgent need to provide a scattering correction method that is different from simulation-based techniques and does not depend on activity images and attenuation images.

[0012] The content in the background section merely discloses technology known only to the inventors and is not intended to represent prior art in the field. Summary of the Invention

[0013] This application aims to provide a scattering correction method, apparatus, digitization device, and computer-readable storage medium to solve at least one problem existing in the prior art.

[0014] According to a first aspect of this application, a scattering correction method is provided, the scattering correction method comprising: acquiring downsampled response lines based on probe data; acquiring an estimated objective function corresponding to each downsampled response line using a moment estimation method based on a delayed step iterative algorithm or an optimized transfer iterative algorithm, wherein the estimated objective function is acquired based on a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, a probability density function of scattered photons, and a probability density function of unscattered photons corresponding to each downsampled response line; solving the estimated objective function to obtain the number of scattering coincidence events corresponding to each downsampled response line; upsampling the downsampled response lines to obtain upsampled response lines; and calculating the number of scattering coincidence events corresponding to each upsampled response line.

[0015] In some embodiments, the downsampled response line is acquired based on probe data, including: acquiring a coincident response line based on the probe data; and downsampling the coincident response line to obtain a downsampled response line; wherein the probe data is acquired based on a target object.

[0016] In some embodiments, based on a delayed iteration algorithm or an optimized transfer iteration algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each downsampled response line, including: based on each coincidence event corresponding to each downsampled response line, obtaining a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra corresponding to each downsampled response line; and based on the two one-dimensional probe energy spectra, using a delayed iteration algorithm or an optimized transfer iteration algorithm to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the corresponding downsampled response line.

[0017] In some embodiments, based on each coincidence event corresponding to each downsampled response line, two one-dimensional detector energy spectra are obtained, including: splitting all coincidence events corresponding to the downsampled response line into single events; dividing the single events into two parts according to the location information of the single events, each part corresponding to a one-dimensional detector energy spectrum; and obtaining two one-dimensional detector energy spectra based on the two parts of single events.

[0018] In some embodiments, based on the two one-dimensional detector energy spectra, a delayed-step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density functions of scattered photons and unscattered photons corresponding to the downsampled response lines. This includes: obtaining a correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum; based on the obtained two one-dimensional detector energy spectra and the correspondence function, using the delayed-step iterative algorithm or the optimized migration iterative algorithm to obtain the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra using the hyperparameter values ​​obtained accordingly; and estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the two downsampled response lines based on the two one-dimensional gamma photon energy spectra.

[0019] In some embodiments, the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum is:

[0020]

[0021] in, X represents the expected value of the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampled response line; X represents the one-dimensional gamma photon energy spectrum; and P represents the fuzzy response matrix corresponding to a single downsampled response line.

[0022] In some embodiments, based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, a delayed-step iterative algorithm or an optimized transfer iterative algorithm and the corresponding acquired hyperparameter values ​​are used to obtain two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra. This includes: constructing a first objective function based on the relational function using a penalized maximum likelihood method; constructing a second objective function based on the first objective function to obtain the corresponding one-dimensional gamma photon energy spectrum based on the maximum value of the first objective function; obtaining the iterative formula of the delayed-step iterative algorithm or the optimized transfer iterative algorithm based on the second objective function; obtaining hyperparameter values ​​through prior information; setting iteration conditions; iterating according to the acquired hyperparameter values ​​using the delayed-step iterative algorithm or the optimized transfer iterative algorithm until the set iteration conditions are met; and estimating the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra using the result corresponding to the maximum value of the first objective function.

[0023] In some embodiments, the iteration condition is that the first objective function reaches its maximum value.

[0024] In some embodiments, the first objective function is:

[0025] Φ(X)=∑ i (-∑ j P ij X j +Y i ln(∑ j Pij X j ))-βR(X),

[0026] Among them, Y i In the diagram, Y represents the one-dimensional detection energy spectrum obtained from scanning the target object, corresponding to a single downsampling response line; i represents the i-th vertical bar region in the energy spectrum; X... i In this context, X represents the one-dimensional gamma photon energy spectrum, and P... ij In this context, P represents the fuzzy response matrix P corresponding to a single downsampled response line. ij Here, β represents the value in the i-th row and j-th column of the fuzzy response matrix corresponding to the downsampled response line, β is a hyperparameter, and R(X) is a penalty term, specifically characterized as follows:

[0027]

[0028] Where Y is the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampling response line, and X represents the one-dimensional gamma photon energy spectrum.

[0029] In some embodiments, the second objective function is:

[0030] X = argmaxΦ(X),

[0031] Where X is a one-dimensional gamma photon energy spectrum.

[0032] In some embodiments, the iterative formula of the delayed iteration algorithm is:

[0033]

[0034] in,

[0035]

[0036]

[0037] Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P... ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to a single downsampled response line. ib The λ represents the value in the i-th row and b-th column of the fuzzy response matrix corresponding to a single downsampled response line, β is a hyperparameter, i represents the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bars in the energy spectrum respectively, k and k+1 are the iteration numbers; EM represents the expectation-maximization algorithm. This is the one-dimensional gamma photon energy spectrum corresponding to the j-th vertical bar region of the energy spectrum obtained based on the k-th iteration of the EM algorithm.

[0038] In some embodiments, the iterative formula of the optimized migration iteration algorithm is:

[0039]

[0040] in,

[0041]

[0042] Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P... ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to a single downsampled response line. ib The values ​​in the i-th row and b-th column of the fuzzy response matrix corresponding to a single downsampled response line are represented by β, where β is a hyperparameter, i represents the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bars in the energy spectrum, respectively, and k and k+1 are the iteration numbers.

[0043] In some embodiments, estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the corresponding downsampled response line based on the two one-dimensional gamma photon energy spectra includes: dividing the one-dimensional gamma photon energy spectrum into a scattered part and an unscattered part; performing fuzzy response processing on the scattered and unscattered parts of the two one-dimensional gamma photon energy spectra to obtain the two scattered parts and the two unscattered parts corresponding to the two one-dimensional detector energy spectra corresponding to the corresponding downsampled response line; performing normalization processing on the two scattered and two unscattered parts corresponding to the two one-dimensional detector energy spectra; and estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the two one-dimensional detector energy spectra corresponding to the corresponding downsampled response line based on the obtained normalized values.

[0044] In some embodiments, the scattering portion of the one-dimensional gamma photon energy spectrum is characterized as follows:

[0045]

[0046] The unscattered portion of the one-dimensional gamma photon energy spectrum is characterized as follows:

[0047]

[0048] in, For the scattering part, This represents the unscattered portion.

[0049] In some embodiments, the one-dimensional gamma photon energy spectrum is divided into a scattering portion and an unscattered portion, including:

[0050] The one-dimensional gamma photon energy spectrum is divided based on the energy value of the gamma photon when it is not scattered. The part with energy value less than the energy value is the scattered part, and the part with energy value equal to the energy value is the unscattered part.

[0051] In some embodiments, the estimated objective function is:

[0052]

[0053] Where σ0 represents the number of true coincidence events, which does not require further processing; σ1+σ2+σ3 represents the number of scattering coincidence events SC, which is an unknown quantity to be determined; the coefficient α 1，m α 2，n ,β 1，m ,β 2，n The calculation method is as follows:

[0054]

[0055]

[0056] in, and It is the probability density function of unscattered photons corresponding to one detector module in the downsampling response line. and It is the scattered photon probability density function corresponding to another detection module in the downsampling response line;

[0057] The calculated σ1+σ2+σ3 values ​​represent the number of scattering coincidence events corresponding to the downsampled response line.

[0058] In some embodiments, upsampling the downsampled response line includes:

[0059] The downsampled response lines are processed using bilinear interpolation, 4D linear interpolation, or 5D linear interpolation to obtain the upsampled response lines corresponding to each downsampled response line.

[0060] In some embodiments, when processing the downsampled response line using a 4D linear interpolation method, the number of scattering coincidence events corresponding to the upsampled response line is calculated using the following formula:

[0061]

[0062] in, The number of scattering coincidence events characterizing the upsampled response line composed of upsampled crystals i and j after 4D linear interpolation; Si This represents the set of downsampling center crystal, downsampling axial adjacent crystal, downsampling radial adjacent crystal, and downsampling relative crystal corresponding to upsampling crystal i; K and L represent the crystal numbers corresponding to the downsampling response lines; Characterize the number of scattering coincidence events on the downsampled response line composed of downsampled crystals K and L; This represents the weight of the downsampling crystal K relative to the upsampling crystal i; W represents the weight of the downsampling crystal L relative to the upsampling crystal j; tot The normalization factor is characterized as follows:

[0063]

[0064] Where N is the number of upsampled response lines contained in a downsampled response line.

[0065] In some embodiments, calculating the number of scattering coincidence events corresponding to each upsampled response line includes: calculating the ratio of the total number of scattering coincidence events on each downsampled response line to the total number of coincidence events; and calculating the number of scattering coincidence events corresponding to the corresponding upsampled response line based on the number of coincidence events on each upsampled response line included in each downsampled response line and the ratio.

[0066] According to a second aspect of this application, a scattering correction method is provided, the scattering correction method comprising: acquiring response lines based on probe data; acquiring an estimated objective function corresponding to each response line using a moment estimation method based on a delayed step iterative algorithm or an optimized transfer iterative algorithm, the estimated objective function being acquired based on a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, a probability density function of scattered photons, and a probability density function of unscattered photons corresponding to each response line; and solving the estimated objective function to obtain the number of scattering coincidence events corresponding to each response line.

[0067] In some embodiments, based on a delayed iteration algorithm or an optimized migration iteration algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each response line, including: based on each coincidence event corresponding to each response line, obtaining a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra corresponding to each response line; based on the two one-dimensional probe energy spectra, using a delayed iteration algorithm or an optimized migration iteration algorithm to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the corresponding response line.

[0068] In some embodiments, obtaining two one-dimensional detector energy spectra based on each coincidence event corresponding to each response line includes: splitting all coincidence events corresponding to the response line into single events; dividing the single events into two parts according to the location information of the single events, with each part corresponding to a one-dimensional detector energy spectrum; and obtaining two one-dimensional detector energy spectra based on the two parts of single events.

[0069] In some embodiments, based on the two one-dimensional detector energy spectra, a delayed-step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density functions of scattered photons and unscattered photons corresponding to the corresponding response lines. This includes: obtaining a correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum; based on the obtained two one-dimensional detector energy spectra and the correspondence function, using the delayed-step iterative algorithm or the optimized migration iterative algorithm to obtain the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra using the hyperparameter values ​​obtained accordingly; and estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the corresponding response lines based on the two one-dimensional gamma photon energy spectra.

[0070] In some embodiments, based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained using a delayed-step iterative algorithm or an optimized transfer iterative algorithm with corresponding hyperparameter values. This includes: constructing a first objective function based on the relational function using a penalized maximum likelihood method; constructing a second objective function based on the first objective function to obtain the corresponding one-dimensional gamma photon energy spectrum by maximizing the first objective function; obtaining the iterative formula of the delayed-step iterative algorithm or the optimized transfer iterative algorithm based on the second objective function; obtaining hyperparameter values ​​through prior information; setting iteration conditions; iterating according to the acquired hyperparameter values ​​using the delayed-step iterative algorithm or the optimized transfer iterative algorithm until the set iteration conditions are met; and estimating the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra using the result corresponding to the maximum value of the first objective function.

[0071] In some embodiments, the iteration condition is that the first objective function reaches its maximum value.

[0072] In some embodiments, estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the corresponding response line based on the two one-dimensional gamma photon energy spectra includes: dividing the one-dimensional gamma photon energy spectrum into a scattered part and an unscattered part; performing fuzzy response processing on the scattered and unscattered parts of the two one-dimensional gamma photon energy spectra to obtain the two scattered parts and the two unscattered parts corresponding to the two one-dimensional detector energy spectra corresponding to the corresponding response line; performing normalization processing on the two recovered scattered parts and the two recovered unscattered parts, and estimating the probability density functions of the two scattered photons and the two unscattered photons corresponding to the two one-dimensional detector energy spectra corresponding to the corresponding response line based on the obtained normalized values.

[0073] In some embodiments, dividing the one-dimensional gamma photon energy spectrum into a scattering portion and an unscattered portion includes: dividing the one-dimensional gamma photon energy spectrum based on the energy value of the gamma photon when it does not scatter, with the portion less than the energy value being the scattering portion and the portion equal to the energy value being the unscattered portion.

[0074] According to a third aspect of this application, an image reconstruction method is provided, the image reconstruction method comprising: obtaining the number of scattering coincidence events corresponding to each response line based on the scattering correction method described in any of the above embodiments; correcting the scattering events based on the number of scattering coincidence events to obtain a reconstructed image.

[0075] According to a fourth aspect of this application, a scattering correction device is provided, the scattering correction device comprising: a downsampled response line acquisition module configured to acquire downsampled response lines based on probe data; an estimation module configured to acquire an estimated objective function corresponding to each downsampled response line using a moment estimation method based on a delayed step iterative algorithm or an optimized transfer iterative algorithm, the estimated objective function being acquired based on a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, a probability density function of scattered photons, and a probability density function of unscattered photons corresponding to each downsampled response line; a scattering coincidence event number acquisition module configured to solve the estimated objective function to acquire the number of scattering coincidence events corresponding to each downsampled response line; an upsampling module configured to perform upsampling processing on the downsampled response lines to acquire upsampled response lines; and a scattering coincidence event number calculation module configured to calculate the number of scattering coincidence events corresponding to each upsampled response line.

[0076] In some embodiments, the estimation module includes: an energy spectrum acquisition module configured to acquire a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra corresponding to each downsampled response line based on each coincidence event corresponding to each downsampled response line; and a probability density acquisition module configured to acquire the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the corresponding downsampled response line based on the two one-dimensional probe energy spectra using a delayed step iterative algorithm or an optimized migration iterative algorithm.

[0077] In some embodiments, the estimation module further includes: a correspondence acquisition module configured to acquire a correspondence function between a one-dimensional detector energy spectrum and a one-dimensional gamma photon energy spectrum; a gamma photon energy spectrum acquisition module configured to acquire two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra based on the acquired two one-dimensional detector energy spectra and the correspondence function, using a delayed step iterative algorithm or an optimized transfer iterative algorithm to obtain the hyperparameter values ​​corresponding to the acquired one-dimensional detector energy spectra; and a probability density estimation module configured to estimate the probability density functions of two scattered photons and two unscattered photons corresponding to the corresponding downsampled response lines based on the two one-dimensional gamma photon energy spectra.

[0078] In some embodiments, the probability density estimation module includes: a partitioning module configured to divide a one-dimensional gamma photon energy spectrum into a scattering portion and an unscattered portion; a fuzzy response recovery module configured to perform fuzzy response recovery processing on the scattering and unscattered portions of the two one-dimensional gamma photon energy spectra to obtain two scattering portions and two unscattered portions corresponding to the two one-dimensional detector energy spectra corresponding to the downsampled response lines; and a density estimation module configured to normalize the two scattering portions and two unscattered portions corresponding to the two one-dimensional detector energy spectra, and estimate the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the obtained normalized values.

[0079] In some embodiments, the gamma photon spectrum acquisition module includes an iterative algorithm iterative formula acquisition module, configured to construct a first objective function based on a correspondence function using a penalized maximum likelihood method; based on the first objective function, construct a second objective function to obtain the corresponding one-dimensional gamma photon spectrum based on the maximum value of the first objective function; based on the second objective function, obtain the iterative formula of a delayed-step iterative algorithm or an optimized transfer iterative algorithm; a hyperparameter value acquisition module, configured to obtain hyperparameter values ​​through prior information; and an iteration module, configured to set iteration conditions, iterate according to the acquired hyperparameter values ​​using the iterative formula of the delayed-step iterative algorithm or the optimized transfer iterative algorithm until the set iteration conditions are met, and estimate the two one-dimensional gamma photon spectra corresponding to the two one-dimensional detector spectra using the result corresponding to the maximum value of the first objective function.

[0080] According to a fifth aspect of this application, a scattering correction device is provided, the scattering correction device comprising: a response line acquisition module configured to acquire response lines based on probe data; an estimation module configured to acquire an estimated objective function corresponding to each response line using a moment estimation method based on a delayed step iterative algorithm or an optimized transfer iterative algorithm, the estimated objective function being acquired based on a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, a probability density function of scattered photons, and a probability density function of unscattered photons corresponding to each response line; and a scattering coincidence event number acquisition module configured to solve the estimated objective function to acquire the number of scattering coincidence events corresponding to each response line.

[0081] According to a sixth aspect of this application, an image reconstruction apparatus is provided, the image reconstruction apparatus comprising: a scattering coincidence event number acquisition module configured to acquire the number of scattering coincidence events corresponding to a response line based on the scattering correction apparatus described in any of the above embodiments; and a reconstruction module configured to perform image reconstruction using an iterative image reconstruction algorithm based on the number of scattering coincidence events, and acquire a reconstructed image.

[0082] According to a seventh aspect of this application, a digital device is provided, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the method described in any of the above embodiments.

[0083] According to an eighth aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the method described in any one of the above embodiments.

[0084] Based on the above embodiments of this application, the beneficial effects of this application include one or more of the following effects in combination:

[0085] In some embodiments, a scheme combining the delayed iteration algorithm (OSL-EDR) or the optimized transfer iteration algorithm (OT-EDR) with the moment estimation method is adopted. Based on the delayed iteration algorithm or the optimized transfer iteration algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each downsampled response line. On the one hand, since the OSL-EDR or OT-EDR algorithm is used for scattering correction in this embodiment, the initial iteration value does not need to be adjusted, and can be set as needed, making scattering correction more convenient. On the other hand, the probability density functions of unscattered photons and scattered photons used in the estimated objective function are not necessarily the same, but are specifically determined according to the two detection modules corresponding to the downsampled response line, so the number of scattering coincidence events corresponding to the downsampled response line is more accurate. Attached Figure Description

[0086] The embodiments of this application are described in detail below with reference to the accompanying drawings. These drawings, which form part of this application, are used to provide a further understanding of the application. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings:

[0087] Figure 1 An exemplary flowchart of a scattering correction method according to an example embodiment of this application is shown;

[0088] Figure 2 This diagram illustrates the calculation of crystal weights in 4D linear interpolation according to an example embodiment of this application.

[0089] Figure 3 An exemplary flowchart of a scattering correction method according to another example embodiment of this application is shown;

[0090] Figure 4 An exemplary flowchart of an image reconstruction method according to an example embodiment of this application is shown;

[0091] Figure 5 An exemplary block diagram of a scattering correction method according to an example embodiment of this application is shown;

[0092] Figure 6 An exemplary block diagram of a scattering correction method according to another example embodiment of this application is shown;

[0093] Figure 7 An exemplary block diagram of an image reconstruction apparatus according to an example embodiment of this application is shown. Detailed Implementation

[0094] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of this application. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0095] In the description of this application, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Furthermore, the terms "first" and "second" are used only for description and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more similar features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0096] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0097] In this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the relative height of the first feature in a certain dimension is higher than that of the second feature. "Below," "below," and "under" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the relative position of the first feature in a certain dimension is smaller than that of the second feature.

[0098] Different embodiments or examples are provided below to implement different structures of this application. To simplify this application, the components and arrangements of specific examples are described below. Of course, these are merely examples and are not intended to limit this application. Reference numerals may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements described. Furthermore, this application provides examples of various specific processes and materials, but those skilled in the art can apply other processes and / or substitute other materials based on the teachings of this application.

[0099] The following description, with reference to the accompanying drawings, illustrates some preferred embodiments of the present application. It should be noted that the following description is for illustrative purposes only and is not intended to limit the scope of protection of this application.

[0100] Figure 1 This is an exemplary flowchart of a scattering correction method according to some embodiments of this application.

[0101] See also Figure 1 The scattering correction method 100 may include the following steps:

[0102] Step S110: Obtain the downsampling response line based on the probe data.

[0103] In some embodiments, the following may be included prior to step S110:

[0104] Step S001: Obtain probe data based on the target object.

[0105] In some embodiments, the target object may be a living object, including but not limited to humans, animals, etc.

[0106] In some embodiments, the detection data may be sampling data obtained based on detector detection and subsequently on a multiple voltage threshold (MVT) method. For example, the detection data may include voltage threshold time pairs. Specifically, the specific design of the detector can be referred to in the prior art, and will not be elaborated here.

[0107] In some embodiments of this application, step S110 may further include the following steps:

[0108] S111, Obtain the response line based on the probe data.

[0109] In some embodiments, the probe data is filtered based on time windows and energy windows to obtain coincident events, thereby obtaining coincident response lines. Specific details can be found in existing technologies, which will not be elaborated upon here.

[0110] S112, perform downsampling processing on the conformal response line to obtain a downsampled response line.

[0111] Those skilled in the art will understand that a response line refers to the connection line between a pair of scintillation crystals in a PET system's detector module pair. Since the number of coincidence events on a single response line may be relatively small during normal scanning, it is difficult to obtain the corresponding energy spectrum based on the coincidence events corresponding to a single response line. Therefore, downsampling processing is required to obtain a downsampled response line. For example, a PET system's detector module pair originally contains 3×3=9 coincidence response lines. After downsampling these 9 response lines, a single downsampled response line is obtained, formed by merging these 9 response lines. Specifically, downsampling processing can merge the response lines included within a single detector module pair, or it can merge the response lines included in multiple adjacent detector module pairs (e.g., two axially adjacent, four axially and radially adjacent, etc.).

[0112] In some specific embodiments, downsampling processing includes merging multiple parallel or angularly aligned response lines that meet preset conditions in terms of spatial location into a single downsampling response line, but is not limited to this. Specific details of downsampling processing can be found in existing technologies and will not be elaborated upon here.

[0113] Step S120: Based on the delayed iteration algorithm or the optimized transfer iteration algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each downsampled response line. The estimated objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons and the probability density function of unscattered photons corresponding to each downsampled response line.

[0114] In this embodiment, the One Step Later (OSL-EDR) iterative algorithm is obtained based on the One Step Later (OSL) method; the Optimization Transfer (OT-EDR) iterative algorithm is obtained based on the Optimization Transfer (OT) method. For details, please refer to the prior art, which will not be elaborated here.

[0115] In some embodiments, step S120 includes:

[0116] Based on each coincidence event corresponding to each downsampled response line, a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra are obtained for each downsampled response line. Based on the two one-dimensional probe energy spectra, a delayed step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the corresponding downsampled response line.

[0117] In some embodiments, the energy spectrum is characterized as a one-dimensional energy histogram, where the horizontal axis represents energy and the total axis represents the gamma photon count. The one-dimensional detection energy spectrum refers to the energy spectrum composed of the energies of gamma photons detected by the detector. It should be understood that the energy spectrum histogram includes multiple vertical bar regions, each of which is called a bin; specific details can be found in existing technologies and will not be elaborated here.

[0118] In some embodiments, based on each coincidence event corresponding to each downsampling response line, two one-dimensional probe energy spectra are obtained, including:

[0119] S1211, splits all coincidence events corresponding to the downsampling response line into single events;

[0120] It should be understood that a coincidence event contains two individual events. Each coincidence event in a downsampled response line is broken down into two corresponding individual events, each containing location information, energy information, and time information.

[0121] S1212, a single event is divided into two parts based on the location information of the single event, and each part corresponds to a one-dimensional detection energy spectrum;

[0122] In some embodiments, the location information of a single event includes the location information of the downsampling detection module that detected the single event. For example, a downsampling response line corresponds to two detection modules A and B, and a portion of the single event included in the downsampling response line corresponds to detection module A, while the other portion corresponds to detection module B.

[0123] S1213, based on the two parts of single event partitioning, obtains two one-dimensional probe energy spectra.

[0124] In some specific examples, based on the detection module information corresponding to a single event, two one-dimensional detection energy spectra corresponding to the downsampled response line can be obtained. Continuing with the example above, one one-dimensional detection energy spectrum can be obtained based on the single event corresponding to detection module A, and the other one-dimensional detection energy spectrum corresponding to the downsampled response line can be obtained based on the single event corresponding to detection module B.

[0125] In some specific embodiments, based on the two one-dimensional detector energy spectra, a delayed-step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density function of the scattered photons and the probability density function of the unscattered photons corresponding to the downsampled response lines, including:

[0126] S1221, the function that obtains the correspondence between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum.

[0127] In some embodiments, the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum is:

[0128]

[0129] in, X represents the expected value of the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampled response line; X represents the one-dimensional gamma photon energy spectrum; and P represents the fuzzy response matrix corresponding to a single downsampled response line.

[0130] In some specific examples, the acquisition of the fuzzy response matrix P corresponding to a single downsampling response line is detailed in existing technologies and will not be elaborated here.

[0131] S1222, based on the two obtained one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained by using a delayed step iterative algorithm or an optimized migration iterative algorithm and the corresponding obtained hyperparameter values.

[0132] In some embodiments, a one-dimensional gamma photon energy spectrum refers to the energy spectrum composed of the energy of the gamma photons themselves.

[0133] In some embodiments, step S1222 includes:

[0134] S122210, based on the correspondence function, construct the first objective function using the panelized maximum likelihood method with penalty; based on the first objective function, construct the second objective function to obtain the corresponding one-dimensional gamma photon energy spectrum based on the maximum value of the first objective function.

[0135] In some embodiments, the first objective function is:

[0136] Φ(X)=∑ i (-∑ j P ij X j +Y i ln(∑ j P ij X j ))-βR(X) (2)

[0137] Among them, Y i In the diagram, Y represents the one-dimensional detection energy spectrum obtained from scanning the target object, corresponding to a single downsampling response line; i represents the i-th vertical bar region in the energy spectrum; X... i In this context, X represents the one-dimensional gamma photon energy spectrum, and P... ij In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij Here, β represents the value in the i-th row and j-th column of the fuzzy response matrix corresponding to the downsampled response line, β is a hyperparameter, and R(X) is a penalty term, specifically characterized as follows:

[0138]

[0139] Where Y is the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampling response line, and X represents the one-dimensional gamma photon energy spectrum.

[0140] In some embodiments, the prior knowledge used to define the penalty term is that the X count of the gamma photon spectrum is low at less than 511 keV, zero at greater than 511 keV, and almost all concentrated at 511 keV.

[0141] In some embodiments, the second objective function is:

[0142] X = argmaxΦ(X) (4)

[0143] Where X is a one-dimensional gamma photon energy spectrum.

[0144] S122220, based on the second objective function, obtain the iterative formula of the delayed method iterative algorithm or the iterative formula of the optimized migration iterative algorithm.

[0145] In some embodiments, the iterative formula of the delayed iteration algorithm is:

[0146]

[0147] in,

[0148]

[0149]

[0150] Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P... ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to the downsampled response line. ib Let be the values ​​of the i-th row and b-th column of the fuzzy response matrix corresponding to the downsampled response line, β be a hyperparameter, i represent the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bar regions in the energy spectrum, and k and k+1 be the iteration numbers.

[0151] In some embodiments, the iterative formula for optimizing the migration iteration algorithm is:

[0152]

[0153] in,

[0154]

[0155] Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P... ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to the downsampled response line. ib Let represent the value in the i-th row and b-th column of the fuzzy response matrix corresponding to the downsampled response line, β be a hyperparameter, i represent the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bar regions in the energy spectrum, k and k+1 be the iteration numbers, and EM be the expectation maximization algorithm. This is the one-dimensional gamma photon energy spectrum corresponding to the j-th vertical bar region of the energy spectrum obtained based on the k-th iteration of the EM algorithm.

[0156] In this embodiment of the application, the OSL-EDR or OT-EDR algorithm is used for scattering correction, which does not require adjustment of the initial iteration value, making scattering correction more convenient.

[0157] S122230, obtains the hyperparameter value β through prior information.

[0158] In some embodiments, the OSL-EDR and OT-EDR algorithms require the selection of an appropriate hyperparameter β to achieve good results. The optimal β needs to be adjusted through preliminary experiments, and different sizes of prostheses require different β values.

[0159] In some embodiments, hyperparameter values ​​can be adjusted experimentally based on a prosthesis, and different prostheses of different sizes require different hyperparameter values, as detailed in existing technologies, which will not be elaborated here. In some specific examples, the prosthesis includes, but is not limited to, point sources or line sources.

[0160] S122240, Set the iteration conditions. Based on the obtained hyperparameter values, iterate until the set iteration conditions are met using the iteration formula of the delayed step method or the iteration formula of the optimized migration method. Estimate the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra by taking the result corresponding to the maximum value of the first objective function.

[0161] In some embodiments, the iteration condition is that the first objective function reaches its maximum value.

[0162] S1223, based on the two one-dimensional gamma photon energy spectra, estimate the probability density functions of the two scattered photons and the probability density functions of the two unscattered photons corresponding to the downsampled response lines.

[0163] In some embodiments, step S1223 includes:

[0164] S122310 divides the one-dimensional gamma photon energy spectrum into a scattered part and an unscattered part.

[0165] In some embodiments, the obtained one-dimensional gamma photon energy spectrum can be divided based on the energy value of the gamma photon when it is not scattered, with the portion below the energy value being the scattered portion and the portion equal to the energy value being the unscattered portion.

[0166] In some specific examples, the resulting one-dimensional gamma photon energy spectrum, X, can be divided into a scattered portion X based on the energy of the unscattered gamma photon, which is 511 keV. sc and the unscattered part X us As shown below:

[0167]

[0168] S122320 performs fuzzy response recovery processing on the scattered and unscattered portions of two one-dimensional gamma photon energy spectra to obtain the two scattered and two unscattered portions corresponding to the two one-dimensional probe energy spectra of the downsampled response lines.

[0169] In some embodiments, X can be obtained based on equation (7). sc and X us Calculate the scattered and unscattered portions of the one-dimensional detector energy spectrum:

[0170] S = PX sc ;

[0171] U = PX us ;

[0172] Where S represents the scattering part of the one-dimensional detector energy spectrum, U represents the unscattered part of the one-dimensional detector energy spectrum, and P is the fuzzy response matrix corresponding to the downsampled response line.

[0173] S122330 normalizes the two scattered and two unscattered portions corresponding to the two one-dimensional detector energy spectra, and estimates the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the obtained normalized values.

[0174] In some embodiments, the two-dimensional instantaneous conformance energy histogram and the two-dimensional delayed conformance energy histogram corresponding to each downsampling response line can be obtained by referring to the prior art, and will not be elaborated here.

[0175] In some embodiments, after obtaining the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons, and the probability density function of unscattered photons corresponding to each downsampled response line, the estimated target function can be obtained.

[0176] In some specific embodiments, the objective function is estimated as follows:

[0177]

[0178] Where σ0 represents the number of true coincidence events, which does not require further processing; σ1+σ2+σ3 represents the number of scattering coincidence events SC, which is an unknown quantity to be determined; the coefficient α 1，m α 2，n ,β 1，m ,β 2，n The calculation method is as follows:

[0179]

[0180]

[0181] in, and It is the probability density function of unscattered photons corresponding to one detector module in the downsampling response line. and It is the scattered photon probability density function corresponding to another detection module in the downsampling response line.

[0182] Step S130: Solve the estimated objective function to obtain the number of scattering coincidence events corresponding to each downsampled response line.

[0183] In some embodiments, the value of σ1+σ2+σ3 obtained by calculating equation (8) is the number of scattering coincidence events corresponding to the downsampled response line.

[0184] In the embodiments of this application, the unscattered photon probability density function in the objective function is estimated. and Not necessarily the same, scattered photon probability density function and They are not necessarily the same, but are determined specifically based on the two detection modules corresponding to the downsampled response line. Based on this, the number of scattering coincidence events corresponding to the downsampled response line is more accurate.

[0185] Step S140: Perform upsampling processing on the downsampled response line to obtain the upsampled response line.

[0186] In some embodiments, upsampling the downsampled response line includes:

[0187] The downsampled response lines are processed using bilinear interpolation, 4D linear interpolation, or 5D linear interpolation to obtain the corresponding upsampled response lines. Specific procedures can be found in existing techniques and will not be elaborated upon here.

[0188] Step S150: Calculate the number of scattering coincidence events corresponding to each upsampled response line.

[0189] In some embodiments, the scintillation crystals included in the detection module of the PET system are referred to as upsampling crystals, and the set of scintillation crystals corresponding to the downsampling response lines obtained by downsampling processing is referred to as downsampling crystals, for example, such as Figure 2 As shown, the downsampling crystal to which the upsampling crystal belongs is denoted as "downsampling center crystal c"; the downsampling crystal that is closest to the upsampling crystal along the axis is denoted as "downsampling axial adjacent crystal a"; the downsampling crystal that is closest to the upsampling crystal in the radial direction is denoted as "downsampling radial adjacent crystal t"; and the downsampling crystal that is closest to the upsampling crystal in the diagonal direction is denoted as "downsampling relative crystal ta".

[0190] like Figure 2 As shown, let the axial length of the downsampling crystal be D. a The radial length is D t An upsampling response line has two upsampling crystals, distinguished by the superscripts "i" and "j". Taking the scintillation crystal labeled "i" as an example, let the radial and axial distances from the center of this upsampling crystal to the center of the "center crystal c" be respectively... The weights of the four downsampling crystals corresponding to one are as follows:

[0191] Downsampling center crystal c”:

[0192] Downsampling axial adjacent crystal a”:

[0193] Downsampling radial adjacent crystal t”:

[0194] Downsampling relative to crystal ta”:

[0195] Similarly, for the four downsampling crystals corresponding to the upsampling crystal with the superscript "j", we also have:

[0196]

[0197]

[0198]

[0199]

[0200] In some specific embodiments, when processing the downsampled response line using the 4D linear interpolation method, the following formula is used to calculate the number of scattering coincidence events corresponding to the upsampled response line:

[0201]

[0202] in, The number of scattering coincidence events characterizing the upsampled response line composed of upsampled crystals i and j after 4D linear interpolation; S i This represents the set of downsampling center crystal, downsampling axial adjacent crystal, downsampling radial adjacent crystal, and downsampling relative crystal corresponding to upsampling crystal i; K and L represent the crystal numbers corresponding to the downsampling response lines; Characterize the number of scattering coincidence events on the downsampled response line composed of downsampled crystals K and L; This represents the weight of the downsampling crystal K relative to the upsampling crystal i; W represents the weight of the downsampling crystal L relative to the upsampling crystal j; tot The normalization factor is characterized as follows:

[0203]

[0204] Where N is the number of upsampled response lines contained in a downsampled response line.

[0205] In some other embodiments, step S150 includes:

[0206] Calculate the ratio of the total number of scattering coincidence events to the total number of coincidence events on each downsampled response line;

[0207] The number of scattering coincidence events corresponding to each upsampled response line is calculated based on the number of coincidence events on each upsampled response line contained in each downsampled response line and the aforementioned proportion.

[0208] Figure 3 This is an exemplary flowchart of a scattering correction method 200 according to some embodiments of this application.

[0209] See also Figure 3 The scattering correction method 200 may include the following steps:

[0210] S210, acquire response lines based on probe data;

[0211] S220, based on the delayed step iterative algorithm or the optimized transfer iterative algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each response line. The estimated objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons and the probability density function of unscattered photons corresponding to each response line.

[0212] S230, Solve the estimated objective function to obtain the number of scattering coincidence events corresponding to each response line.

[0213] Unlike the scattering correction method 100, which obtains a response line based on probe data, downsamples the response line to obtain a downsampled response line, uses a delayed iterative algorithm or an optimized transfer iterative algorithm combined with a matrix estimation method to obtain the number of scattering coincidence events corresponding to the downsampled response line, and then upsamples the downsampled response line to obtain the number of scattering coincidence events for each response line, this embodiment directly processes the response line obtained based on probe data using a delayed iterative algorithm or an optimized transfer iterative algorithm combined with a matrix estimation method to obtain the number of scattering coincidence events for each response line.

[0214] In the embodiments of this application, the scattering correction method 200 may selectively combine features of the scattering correction method 100 or other methods, or vice versa.

[0215] Figure 4 This is an exemplary flowchart of an image reconstruction method according to some embodiments of this application.

[0216] See also Figure 4 The image reconstruction method 300 may include the following steps:

[0217] S310, the scattering correction method described in the above embodiments obtains the number of scattering coincidence events corresponding to each upsampled response line;

[0218] S320 corrects the scattering events based on the number of scattering coincidence events to obtain a reconstructed image.

[0219] In some embodiments, an iterative image reconstruction algorithm can be used to reconstruct the image based on the number of scattering coincidence events, thereby obtaining the reconstructed image.

[0220] For details of step S320, please refer to the existing technology, and will not be repeated here.

[0221] Figure 5 This is an exemplary block diagram of a scattering correction device according to some embodiments of this application. For example... Figure 5 As shown, the scattering correction device 400 may include:

[0222] The downsampling response line acquisition module 410 is configured to acquire the downsampling response line based on the probe data;

[0223] The estimation module 420 is configured to use a moment estimation method to obtain the estimation objective function corresponding to each downsampled response line based on a delayed step iterative algorithm or an optimized transfer iterative algorithm. The estimation objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons, and the probability density function of unscattered photons corresponding to each downsampled response line.

[0224] The scattering coincidence event acquisition module 430 is configured to solve the estimated objective function and acquire the number of scattering coincidence events corresponding to each downsampled response line.

[0225] Upsampling module 440 is configured to perform upsampling processing on downsampling response line to obtain upsampling response line;

[0226] The scattering coincidence event count calculation module 450 is configured to calculate the number of scattering coincidence events corresponding to each upsampled response line.

[0227] In some embodiments, the estimation module 420 includes:

[0228] The energy spectrum acquisition module is configured to acquire a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra for each downsampled response line based on each coincidence event corresponding to each downsampled response line.

[0229] The probability density acquisition module is configured to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the downsampled response lines based on the two one-dimensional probe energy spectra using a delayed step iterative algorithm or an optimized migration iterative algorithm.

[0230] In some embodiments, the estimation module 420 further includes:

[0231] The correspondence acquisition module is configured to acquire the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum;

[0232] The gamma photon energy spectrum acquisition module is configured to acquire two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, using a delayed step iterative algorithm or an optimized migration iterative algorithm to acquire the corresponding hyperparameter values.

[0233] The probability density estimation module is configured to estimate the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the two one-dimensional gamma photon energy spectra.

[0234] In some embodiments, the probability density estimation module includes:

[0235] The partitioning module is configured to divide the one-dimensional gamma photon energy spectrum into a scattering part and an unscattered part.

[0236] The fuzzy response recovery module is configured to perform fuzzy response recovery processing on the scattered and unscattered parts of the two one-dimensional gamma photon energy spectra, and obtain the two scattered and two unscattered parts corresponding to the two one-dimensional probe energy spectra corresponding to the downsampled response lines.

[0237] The density estimation module is configured to normalize the two scattered and two unscattered portions corresponding to the two one-dimensional probe energy spectra, and estimate the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the obtained normalized values.

[0238] In some embodiments, the gamma photon energy spectrum acquisition module includes an iterative algorithm iterative formula acquisition module, which is configured to construct a first objective function based on a correspondence function using a penalized maximum likelihood method; based on the first objective function, construct a second objective function to obtain the corresponding one-dimensional gamma photon energy spectrum based on the maximum value of the first objective function; and based on the second objective function, obtain the iterative formula of the delayed method iterative algorithm or the iterative formula of the optimized transfer iterative algorithm.

[0239] The hyperparameter value acquisition module is configured to acquire hyperparameter values ​​through prior information.

[0240] The iteration module is configured to set iteration conditions, and based on the acquired hyperparameter values, it iterates until the set iteration conditions are met using either the delayed iteration algorithm or the optimized migration iteration algorithm. The result corresponding to the maximum value of the first objective function is used to estimate the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra.

[0241] Figure 6 This is an exemplary block diagram of a scattering correction device according to some embodiments of this application. For example... Figure 6 As shown, the scattering correction device 500 may include:

[0242] The response line acquisition module 510 is configured to acquire the response line based on the probe data;

[0243] The estimation module 520 is configured to use a moment estimation method to obtain the estimation objective function corresponding to each response line based on a delayed step iterative algorithm or an optimized transfer iterative algorithm. The estimation objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons, and the probability density function of unscattered photons corresponding to each response line.

[0244] The scattering coincidence event acquisition module 530 is configured to solve the estimated objective function and acquire the number of scattering coincidence events corresponding to each response line.

[0245] Unlike the embodiment of scattering correction device 400, which obtains response lines based on probe data, downsamples the response lines to obtain downsampled response lines, obtains the number of scattering coincidence events corresponding to the downsampled response lines based on a delayed iterative algorithm or an optimized transfer iterative algorithm combined with a matrix estimation method, and then upsamples the downsampled response lines to obtain the number of scattering coincidence events for each response line, this embodiment directly processes the response lines obtained based on probe data using a delayed iterative algorithm or an optimized transfer iterative algorithm combined with a matrix estimation method to obtain the number of scattering coincidence events corresponding to each response line.

[0246] In the embodiments of this application, the scattering correction device 500 can be used to implement the scattering correction method 200 or the method described in other embodiments herein, and can be selectively combined with the features of the scattering correction device 400 or other devices, or selectively combined with the features of the scattering correction method 100 or 200 or other methods, and vice versa.

[0247] Figure 7 These are exemplary block diagrams of an image reconstruction apparatus according to some embodiments of this application. Figure 7 As shown, the image reconstruction apparatus 600 may include:

[0248] The scattering coincidence event acquisition module 610 is configured to acquire the number of scattering coincidence events corresponding to each response line based on the scattering correction method described in any of the above embodiments.

[0249] The reconstruction module 620 is configured to correct scattering events based on the number of scattering coincidence events and obtain a reconstructed image.

[0250] In the embodiments of this application, the image reconstruction apparatus 600 can be used to implement the image reconstruction method 300 or the methods described in other embodiments herein, and can selectively combine features of the image reconstruction method 300 or other methods, or vice versa.

[0251] In some embodiments of this application, the image reconstruction apparatus 600 may also include components or features of the scattering correction apparatus 400, 500 in a manner that is not contradictory, and vice versa.

[0252] In some embodiments, this application also provides a digitizing device, which includes the apparatus described in any one of the above embodiments.

[0253] In some embodiments, this application also provides a digital device that may include a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, can implement the steps of the method described in any of the above embodiments.

[0254] Although not shown, some embodiments also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in any of the above embodiments. The computer program includes various program modules / units constituting the apparatus according to embodiments of this application, and when executed, the computer program comprised of these program modules / units is capable of performing functions corresponding to the various steps in the methods described in the above embodiments. The computer program can also run on electronic devices as described in embodiments of this application.

[0255] The basic concepts have been described herein. It is obvious that the detailed disclosure above is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, various modifications, improvements, and corrections may be made to this application by those skilled in the art. Such modifications, improvements, and corrections are suggested in this application and therefore remain within the spirit and scope of the exemplary embodiments of this application.

[0256] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this application do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0257] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Accordingly, aspects of this application can be implemented entirely by hardware, entirely by software (including firmware, resident software, microcode, etc.), or by a combination of hardware and software. All of the above hardware or software may be referred to as a “data block,” “module,” “engine,” “unit,” “component,” or “system.” Furthermore, aspects of this application may manifest as a computer product located on one or more computer-readable media, the product including computer-readable program code.

[0258] Computer storage media may contain a propagated data signal containing computer program code, for example, on baseband or as part of a carrier wave. This propagated signal may take various forms, including electromagnetic, optical, and suitable combinations thereof. Computer storage media can be any computer-readable medium other than a computer-readable storage medium, which can be connected to an instruction execution system, apparatus, or device to enable communication, propagation, or transmission of a program for use. The program code located on the computer storage medium can be propagated through any suitable medium, including radio, cable, fiber optic cable, RF, or similar media, or any combination of the above media.

[0259] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, Python, etc., conventional procedural programming languages ​​such as C, Visual Basic, Fortran 2003, Perl, COBOL 2002, PHP, ABAP, dynamic programming languages ​​such as Python, Ruby, and Groovy, or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer through any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0260] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although the foregoing disclosure has discussed some currently considered useful embodiments of the invention through various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, while the system components described above can be implemented using hardware devices, they can also be implemented solely through software solutions, such as installing the described system on existing servers or mobile devices.

[0261] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this disclosure method does not imply that the subject matter of the application requires more features than those mentioned in the claims. In fact, the embodiments contain fewer features than all the features of the single embodiments disclosed above.

[0262] In some embodiments, numbers describing the quantity of components and attributes are used. It should be understood that such numbers used in the description of embodiments are modified in some examples with the terms "approximately," "approximately," or "generally." Unless otherwise stated, "approximately," "approximately," or "generally" indicates that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the characteristics required by individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of scope in some embodiments of this application are approximate values, in specific embodiments, such values ​​are set as precisely as feasible.

[0263] For each patent, patent application, patent application publication, and other material such as articles, books, specifications, publications, and documents referenced in this application, the entire contents of that patent are incorporated herein by reference. This excludes historical application documents that are inconsistent with or conflict with the content of this application, as well as documents that limit the broadest scope of the claims in this application (currently or subsequently appended to this application). It should be noted that if there are any inconsistencies or conflicts between the descriptions, definitions, and / or terminology used in the supplementary materials of this application and the content of this application, the descriptions, definitions, and / or terminology used in this application shall prevail.

[0264] Finally, it should be noted that the above descriptions are merely exemplary embodiments of this application and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A scattering correction method, characterized in that, The scattering correction method includes: Obtain the downsampling response line based on the probe data; Based on the delayed step iterative algorithm or the optimized transfer iterative algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each downsampled response line. The estimated objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons and the probability density function of unscattered photons corresponding to each downsampled response line. Solve the estimated objective function to obtain the number of scattering coincidence events corresponding to each downsampled response line; The downsampled response line is upsampled to obtain the upsampled response line; Calculate the number of scattering coincidence events corresponding to each upsampled response line.

2. The scattering correction method according to claim 1, characterized in that, The downsampling response line is acquired based on the probe data and includes: Obtain the response line based on the probe data; The coincident response line is downsampled to obtain a downsampled response line; The detection data is obtained based on the target object.

3. The scattering correction method according to claim 1, characterized in that, Based on the delayed iterative algorithm or the optimized transfer iterative algorithm, the estimated objective function corresponding to each downsampled response line is obtained using the moment estimation method, including: Based on each coincidence event corresponding to each downsampled response line, a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra are obtained for each downsampled response line. Based on the two one-dimensional probe energy spectra, a delayed step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the corresponding downsampled response line.

4. The scattering correction method according to claim 3, characterized in that, Based on the coincidence events corresponding to each downsampling response line, two one-dimensional probe energy spectra are obtained, including: Break down all coincidence events corresponding to the downsampling response line into single events; Based on the location information of a single event, the single event is divided into two parts, and each part corresponds to a one-dimensional detection energy spectrum. Based on the two parts of single events, two one-dimensional probe energy spectra are obtained.

5. The scattering correction method according to claim 3, characterized in that, Based on the two one-dimensional detector energy spectra, the probability density functions of scattered photons and unscattered photons corresponding to the downsampled response lines are obtained using a delayed-step iterative algorithm or an optimized migration iterative algorithm, including: Obtain the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum; Based on the two obtained one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained by using the delayed step iterative algorithm or the optimized migration iterative algorithm with the corresponding hyperparameter values. Based on the two one-dimensional gamma photon energy spectra, the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines are estimated.

6. The scattering correction method according to claim 5, characterized in that, The correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum is: in, X represents the expected value of the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampled response line; X represents the one-dimensional gamma photon energy spectrum; and P represents the fuzzy response matrix corresponding to a single downsampled response line.

7. The scattering correction method according to claim 5, characterized in that, Based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained using a delayed step iterative algorithm or an optimized migration iterative algorithm and the corresponding acquired hyperparameter values, including: Based on the correspondence function, a first objective function is constructed using the penalized maximum likelihood method; based on the first objective function, a second objective function is constructed to obtain the corresponding one-dimensional gamma photon energy spectrum by maximizing the first objective function. Based on the second objective function, obtain the iterative formula of the delayed step iterative algorithm or the iterative formula of the optimized migration iterative algorithm; Obtain hyperparameter values ​​using prior information; Set the iteration conditions, and based on the obtained hyperparameter values, iterate until the set iteration conditions are met by using the iteration formula of the delayed step method or the iteration formula of the optimized transfer method. Estimate the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra by using the result corresponding to the maximum value of the first objective function.

8. The scattering correction method according to claim 7, characterized in that, The iteration condition is that the first objective function reaches its maximum value.

9. The scattering correction method according to claim 7, characterized in that, The first objective function is: Φ(X)=∑ i (-∑ j P ij X j +Y i ln(∑ j P ij X j ))-βR(X), Among them, Y i In the diagram, Y represents the one-dimensional detection energy spectrum obtained from scanning the target object, corresponding to a single downsampling response line; i represents the i-th vertical bar region in the energy spectrum; and X... i In this context, X represents the one-dimensional gamma photon energy spectrum, and P... ij In this context, P represents the fuzzy response matrix P corresponding to a single downsampled response line. ij Here, β represents the value in the i-th row and j-th column of the fuzzy response matrix corresponding to the downsampled response line, β is a hyperparameter, and R(X) is a penalty term, specifically characterized as follows: Where Y is the one-dimensional detector energy spectrum obtained by scanning the target object corresponding to a single downsampling response line, and X represents the one-dimensional gamma photon energy spectrum.

10. The scattering correction method according to claim 7, characterized in that, The second objective function is: X = argmaxΦ(X), Where X is a one-dimensional gamma photon energy spectrum.

11. The scattering correction method according to claim 7, characterized in that, The iterative formula for the one-step-later iterative algorithm is: in, Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to a single downsampled response line. ib The λ represents the value in the i-th row and b-th column of the fuzzy response matrix corresponding to a single downsampled response line, β is a hyperparameter, i represents the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bars in the energy spectrum respectively, k and k+1 are the iteration numbers; EM represents the expectation-maximization algorithm. This is the one-dimensional gamma photon energy spectrum corresponding to the j-th vertical bar region of the energy spectrum obtained based on the k-th iteration of the EM algorithm.

12. The scattering correction method according to claim 7, characterized in that, The iterative formula for the optimized migration iteration algorithm is: in, Where Y represents the one-dimensional detector energy spectrum based on scanning of the target object corresponding to a single downsampling response line; X represents the one-dimensional gamma photon energy spectrum; and P ij P ib In this context, P represents the fuzzy response matrix corresponding to a single downsampled response line. ij P represents the value of the i-th row and j-th column of the fuzzy response matrix corresponding to a single downsampled response line. ib The values ​​in the i-th row and b-th column of the fuzzy response matrix corresponding to a single downsampled response line are represented by β, where β is a hyperparameter, i represents the i-th vertical bar region in the energy spectrum, b and j represent the b-th and j-th vertical bars in the energy spectrum, respectively, and k and k+1 are the iteration numbers.

13. The scattering correction method according to claim 5, characterized in that, Based on the two one-dimensional gamma photon energy spectra, the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines are estimated, including: The one-dimensional gamma photon energy spectrum is divided into a scattered part and an unscattered part; By performing fuzzy response processing on the scattered and unscattered portions of two one-dimensional gamma photon energy spectra, the two scattered and two unscattered portions corresponding to the two one-dimensional detector energy spectra corresponding to the downsampled response lines are obtained; The two scattered and two unscattered portions corresponding to the two one-dimensional detector energy spectra are normalized. Based on the obtained normalized values, the probability density functions of the two scattered photons and the two unscattered photons corresponding to the two one-dimensional detector energy spectra of the downsampled response lines are estimated.

14. The scattering correction method according to claim 13, characterized in that, The scattering component of the one-dimensional gamma photon energy spectrum is characterized as follows: The unscattered portion of the one-dimensional gamma photon energy spectrum is characterized as follows: in, The scattering part, This represents the unscattered portion.

15. The scattering correction method according to claim 13, characterized in that, The one-dimensional gamma photon energy spectrum is divided into a scattered part and an unscattered part, including: The one-dimensional gamma photon energy spectrum is divided based on the energy value of the gamma photon when it is not scattered. The part with energy value less than the energy value is the scattered part, and the part with energy value equal to the energy value is the unscattered part.

16. The scattering correction method according to claim 1, characterized in that, The estimated objective function is: Where σ0 represents the number of true coincidence events, which does not require further processing; σ1+σ2+σ3 represents the number of scattering coincidence events SC, which is an unknown quantity to be determined; the coefficient α 1,m ,α 2,n ,β 1,m ,β 2,n The calculation method is as follows: in, and It is the probability density function of unscattered photons corresponding to one detector module in the downsampling response line. and It is the scattered photon probability density function corresponding to another detection module in the downsampling response line; The calculated σ1+σ2+σ3 values ​​represent the number of scattering coincidence events corresponding to the downsampled response line.

17. The scattering correction method according to claim 1, characterized in that, Upsampling is performed on the downsampled response line, including: The downsampled response lines are processed using bilinear interpolation, 4D linear interpolation, or 5D linear interpolation to obtain the upsampled response lines corresponding to each downsampled response line.

18. The scattering correction method according to claim 17, characterized in that, When processing the downsampled response line using the 4D linear interpolation method, the number of scattering coincidence events corresponding to the upsampled response line is calculated using the following formula: in, The number of scattering coincidence events characterizing the upsampled response line composed of upsampled crystals i and j after 4D linear interpolation; S i This represents the set of downsampling center crystal, downsampling axial adjacent crystal, downsampling radial adjacent crystal, and downsampling relative crystal corresponding to upsampling crystal i; K and L represent the crystal numbers corresponding to the downsampling response lines; Characterize the number of scattering coincidence events on the downsampled response line composed of downsampled crystals K and L; This represents the weight of the downsampling crystal K relative to the upsampling crystal i; W represents the weight of the downsampling crystal L relative to the upsampling crystal j; tot The normalization factor is characterized as follows: Where N is the number of upsampled response lines contained in a downsampled response line.

19. The scattering correction method according to claim 1, characterized in that, Calculate the number of scattering coincidence events corresponding to each upsampled response line, including: Calculate the ratio of the total number of scattering coincidence events to the total number of coincidence events on each of the downsampled response lines; The number of scattering coincidence events corresponding to each upsampled response line is calculated based on the number of coincidence events on each upsampled response line contained in each downsampled response line and the proportion.

20. A scattering correction method, characterized in that, The scattering correction method includes: Response lines are obtained based on probe data; Based on the delayed step iterative algorithm or the optimized transfer iterative algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each response line. The estimated objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons and the probability density function of unscattered photons corresponding to each response line. Solve the estimated objective function to obtain the number of scattering coincidence events corresponding to each response line.

21. The scattering correction method according to claim 20, characterized in that, Based on the delayed iterative algorithm or the optimized transfer iterative algorithm, the moment estimation method is used to obtain the estimated objective function corresponding to each response line, including: Based on each coincidence event corresponding to each response line, a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra are obtained for each response line. Based on the two one-dimensional probe energy spectra, a delayed step iterative algorithm or an optimized migration iterative algorithm is used to obtain the probability density function of the scattered photons and the probability density function of the unscattered photons corresponding to the corresponding response lines.

22. The scattering correction method according to claim 21, characterized in that, Based on the coincidence events corresponding to each response line, two one-dimensional probe energy spectra are obtained, including: Break down all matching events corresponding to the response line into single events; Based on the location information of a single event, the single event is divided into two parts, and each part corresponds to a one-dimensional detection energy spectrum. Based on the two parts of single events, two one-dimensional probe energy spectra are obtained.

23. The scattering correction method according to claim 21, characterized in that, Based on the two one-dimensional detector energy spectra, the probability density functions of scattered photons and unscattered photons corresponding to the respective response lines are obtained using a delayed-step iterative algorithm or an optimized migration iterative algorithm, including: Obtain the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum; Based on the two obtained one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained by using the delayed step iterative algorithm or the optimized migration iterative algorithm with the corresponding hyperparameter values. Based on the two one-dimensional gamma photon energy spectra, the probability density functions of the two scattered photons and the two unscattered photons corresponding to the corresponding response lines are estimated.

24. The scattering correction method according to claim 23, characterized in that, Based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra are obtained using a delayed step iterative algorithm or an optimized migration iterative algorithm with corresponding hyperparameter values, including: Based on the correspondence function, a first objective function is constructed using the penalized maximum likelihood method; based on the first objective function, a second objective function is constructed to obtain the corresponding one-dimensional gamma photon energy spectrum by maximizing the first objective function. Based on the second objective function, obtain the iterative formula of the delayed step iterative algorithm or the iterative formula of the optimized migration iterative algorithm; Obtain hyperparameter values ​​using prior information; Set the iteration conditions, and based on the obtained hyperparameter values, iterate until the set iteration conditions are met by using the iteration formula of the delayed step method or the iteration formula of the optimized transfer method. Estimate the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra by using the result corresponding to the maximum value of the first objective function.

25. The scattering correction method according to claim 24, characterized in that, The iteration condition is that the first objective function reaches its maximum value.

26. The scattering correction method according to claim 23, characterized in that, Based on the two one-dimensional gamma photon energy spectra, the probability density functions of the two scattered photons and the two unscattered photons corresponding to the corresponding response lines are estimated, including: The one-dimensional gamma photon energy spectrum is divided into a scattered part and an unscattered part; By performing fuzzy response processing on the scattered and unscattered portions of two one-dimensional gamma photon energy spectra, the two scattered and two unscattered portions corresponding to the two one-dimensional detector energy spectra of the corresponding response lines are obtained; The two recovered scattered portions and the two recovered unscattered portions are normalized, and the probability density functions of the two scattered photons and the two unscattered photons corresponding to the two one-dimensional detector energy spectra of the corresponding response lines are estimated based on the obtained normalized values.

27. The scattering correction method according to claim 26, characterized in that, The one-dimensional gamma photon energy spectrum is divided into a scattered part and an unscattered part, including: The one-dimensional gamma photon energy spectrum is divided based on the energy value of the gamma photon when it is not scattered. The part with energy value less than the energy value is the scattered part, and the part with energy value equal to the energy value is the unscattered part.

28. An image reconstruction method, characterized in that, The image reconstruction method includes: The number of scattering coincidence events corresponding to each response line is obtained based on the scattering correction method according to any one of claims 1-27; The scattering events are corrected based on the number of scattering coincidence events to obtain a reconstructed image.

29. A scattering correction device, characterized in that, The scattering correction device includes: The downsampling response line acquisition module is configured to acquire the downsampling response line based on the probe data; The estimation module is configured to use a moment estimation method to obtain the estimation objective function corresponding to each downsampled response line based on a delayed step iterative algorithm or an optimized transfer iterative algorithm. The estimation objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons, and the probability density function of unscattered photons corresponding to each downsampled response line. The scattering coincidence event acquisition module is configured to solve the estimated objective function and obtain the number of scattering coincidence events corresponding to each downsampled response line. The upsampling module is configured to perform upsampling processing on the downsampling response line to obtain the upsampling response line; The scattering coincidence event count calculation module is configured to calculate the number of scattering coincidence events corresponding to each upsampled response line.

30. The scattering correction device according to claim 29, characterized in that, The estimation module includes: The energy spectrum acquisition module is configured to acquire a two-dimensional instantaneous coincidence energy histogram, a two-dimensional delayed coincidence energy histogram, and two one-dimensional probe energy spectra for each downsampled response line based on each coincidence event corresponding to each downsampled response line. The probability density acquisition module is configured to obtain the probability density function of scattered photons and the probability density function of unscattered photons corresponding to the downsampled response lines based on the two one-dimensional probe energy spectra using a delayed step iterative algorithm or an optimized migration iterative algorithm.

31. The scattering correction device according to claim 29, characterized in that, The estimation module also includes: The correspondence acquisition module is configured to acquire the correspondence function between the one-dimensional detector energy spectrum and the one-dimensional gamma photon energy spectrum; The gamma photon energy spectrum acquisition module is configured to acquire two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra based on the acquired two one-dimensional detector energy spectra and their corresponding relational functions, using a delayed step iterative algorithm or an optimized migration iterative algorithm to acquire the corresponding hyperparameter values. The probability density estimation module is configured to estimate the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the two one-dimensional gamma photon energy spectra.

32. The scattering correction device according to claim 31, characterized in that, The probability density estimation module includes: The partitioning module is configured to divide the one-dimensional gamma photon energy spectrum into a scattering part and an unscattered part. The fuzzy response recovery module is configured to perform fuzzy response recovery processing on the scattered and unscattered parts of the two one-dimensional gamma photon energy spectra, and obtain the two scattered and two unscattered parts corresponding to the two one-dimensional probe energy spectra corresponding to the downsampled response lines. The density estimation module is configured to normalize the two scattered and two unscattered portions corresponding to the two one-dimensional probe energy spectra, and estimate the probability density functions of the two scattered photons and the two unscattered photons corresponding to the downsampled response lines based on the obtained normalized values.

33. The scattering correction device according to claim 31, characterized in that, The gamma photon energy spectrum acquisition module includes an iterative algorithm iterative formula acquisition module, which is configured to construct the first objective function based on the correspondence function using the penalized maximum likelihood method; Based on the first objective function, a second objective function is constructed to obtain the corresponding one-dimensional gamma photon energy spectrum based on the maximum value of the first objective function. Based on the second objective function, obtain the iterative formula of the delayed step iterative algorithm or the iterative formula of the optimized migration iterative algorithm; The hyperparameter value acquisition module is configured to acquire hyperparameter values ​​through prior information; The iteration module is configured to set iteration conditions, and based on the acquired hyperparameter values, it iterates until the set iteration conditions are met using either the delayed iteration algorithm or the optimized migration iteration algorithm. The result corresponding to the maximum value of the first objective function is used to estimate the two one-dimensional gamma photon energy spectra corresponding to the two one-dimensional detector energy spectra.

34. A scattering correction device, characterized in that, The scattering correction device includes: The response line acquisition module is configured to acquire the response line based on the probe data. The estimation module is configured to use a moment estimation method to obtain the estimation objective function corresponding to each response line based on a delayed step iterative algorithm or an optimized transfer iterative algorithm. The estimation objective function is obtained based on the two-dimensional instantaneous coincidence energy histogram, the two-dimensional delayed coincidence energy histogram, the probability density function of scattered photons, and the probability density function of unscattered photons corresponding to each response line. The scattering coincidence event acquisition module is configured to solve the estimated objective function and obtain the number of scattering coincidence events corresponding to each response line.

35. An image reconstruction apparatus, characterized in that, The image reconstruction apparatus includes: A module for obtaining the number of scattering coincidence events is configured to obtain the number of scattering coincidence events corresponding to the response line based on the scattering correction device according to any one of claims 29-34; The reconstruction module is configured to use an iterative image reconstruction algorithm based on the number of scattering coincidence events to reconstruct the image and obtain the reconstructed image.

36. A digital device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the method as claimed in any one of claims 1 to 28.

37. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 28.

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