Systems and methods for generating denoised spectral CT images from spectral CT image data acquired using a spectral CT imaging system

Abstract

Denoise spectral CT image data. A denoising linear estimate of spectral CT image data is determined by maximizing or minimizing a first objective function. At least one parameter of the denoising linear estimate is determined by at least one machine learning system. The denoiser is based on a linear minimum mean square error (LMMSE) estimator. While LMMSE is very fast to compute, it is not commonly used for CT image denoising due to its inability to adapt to different amounts of denoising for different images and the difficulty of deriving accurate statistical characteristics from CT image data. To overcome these issues, model-based deep learning models, such as deep neural networks that retain the model-based LMMSE structure, have been proposed.

Description

[Technical Field]

[0001] FIELD OF THE INVENTION Embodiments of the subject matter disclosed herein relate to X-ray technology and X-ray imaging, and corresponding image reconstruction and imaging tasks. In particular, embodiments of the subject matter disclosed herein relate to systems and methods for generating denoised spectral CT (computed tomography) images from spectral CT image data acquired using a spectral (energy-resolved) CT imaging system. [Background technology]

[0002] X-ray imaging systems, such as CT (Computed Tomography) imaging systems and more general X-ray imaging systems, have been used for many years in medical applications such as medical diagnosis and treatment.

[0003] X-ray imaging systems, such as CT imaging systems, typically include an X-ray source and an X-ray detector, which includes multiple detector modules, each consisting of one or more detector elements, for independently measuring X-ray intensity. The X-ray source emits X-rays, which are received by the detector after passing through the subject or object being imaged. Typical medical X-ray tubes have a wide energy spectrum, ranging from zero to 160 keV. Therefore, X-ray detectors typically detect X-rays at a variety of energy levels.

[0004] The x-ray source and x-ray detector are typically positioned on a rotating member in a gantry that rotates around the subject or object. The emitted x-rays are attenuated as they pass through the subject or object, and the resulting transmitted x-rays are measured by the detector. The measured data is used to reconstruct an image of the subject or object.

[0005] The challenge for X-ray detectors is to extract maximum information from the detected X-rays and inject it into an image of the object or specimen. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] US Patent Application Publication No. 2018 / 0293762 Summary of the Invention

[0007] It may be useful to provide a brief overview of an exemplary general x-ray imaging system according to the prior art with reference to Figure 1A. In this exemplary embodiment, x-ray imaging system 100 includes an x-ray source 10, an x-ray detector 20, and an associated image processing system 30. In general, x-ray detector 20 is configured to register radiation from x-ray source 10 that has passed through an object, specimen, or portion thereof, and is optionally focused by x-ray optics or collimators. x-ray detector 20 is connectable to image processing system 30 via suitable readout electronics, at least a portion of which is incorporated within x-ray detector 20, to enable image processing and / or image reconstruction by image processing system 30.

[0008] Conventional CT imaging systems include an X-ray source and an X-ray detector positioned to acquire projection images of a subject or object at different view angles covering at least 180 degrees. This is most commonly achieved by mounting the X-ray source and detector on a support that can rotate around the subject or object, such as a rotating member of a gantry. An image containing projections recorded on different detector elements for different view angles is called a sinogram. Hereinafter, even if the detector is two-dimensional, the collection of projections recorded on different detector elements for different view angles will be referred to as a sinogram, and the sinogram will be considered a three-dimensional image.

[0009] FIG. 1B is a schematic diagram illustrating an example of a prior art X-ray imaging system setup, showing projection lines from an X-ray source, through an object, to an X-ray detector.

[0010] A further development of X-ray imaging is energy-resolved X-ray imaging, also known as spectral X-ray imaging. This can be achieved by rapidly switching the X-ray source between two different emission spectra, by using two or more X-ray sources that emit different X-ray spectra, or by using an energy-discriminating detector which measures the incoming radiation in two or more energy levels. One example of such a detector is a multi-bin photon-counting detector, in which each recorded photon generates a current pulse that is compared to a series of thresholds to count the number of photons incident on each of several energy bins.

[0011] Spectral X-ray projection measurements obtain projection images at each energy level. The weighted sum of these projection images is described in "SNR and DQE analysis of broad spectrum X-ray imaging", Tapiovaara and Wagner, Phys. Med. Biol. 30, 519.

[0012] Another technique enabled by energy-resolved X-ray imaging is basis material decomposition, which exploits the fact that all materials composed of elements with low atomic numbers, such as human tissue, have linear attenuation coefficients whose energy dependence can be approximately expressed as a linear combination of two (or more) basis functions. μ(E)=a1f1(E)+a2f2(E) where f1 and f2 are basis functions and a1 and a2 are the corresponding basis coefficients. More generally, f i is the basis function, a iare the corresponding basis coefficients, i = 1,...,N, where N is the total number of basis functions. If there are one or more elements in the imaging volume with sufficiently high atomic numbers that their K-absorption edges lie in the energy range used for imaging, then one basis function must be added for each such element. In medical imaging, such K-edge elements would typically be iodine or gadolinium, substances used as contrast agents.

[0013] Basis material decomposition is described in "Energy-selective reconstructions in X-ray computerized tomography", Alvarez, Macovski, Phys Med Biol. 1976; 21(5):733-744. In the basis material decomposition, the integral of each basis coefficient is given by, for i=1,...,N (N is the number of basis functions):

number

number

[0014] Next, under the assumption that the counts in each bin are Poisson-distributed random variables, we use the maximum likelihood method to calculate A i can be estimated. This is achieved by minimizing the negative log-likelihood function. See, for example, "K-edge imaging in X-ray computed tomography using multi-bin photon counting detectors," Roessl and Proksa, Phys. Med. Biol. 52 (2007), 4679-4696.

number

[0015] the result,

number

[0016] Standard data management procedures for X-ray imaging systems present various approaches to optimize data acquisition, sometimes at the expense of spatial resolution, noise level, and / or system complexity.

[0017] Basis coefficient a inside the object i The map is called a basis material image, a basis image, a material image, a material-specific image, a material map or a basis map.

[0018] However, a well-known limitation of this technique is that the variance of the estimated line integrals normally increases with the number of bases used in the basis decomposition, which, among other things, results in an unfortunate trade-off between improved tissue quantification and increased image noise.

[0019] Furthermore, performing an accurate basis decomposition using more than two basis functions is difficult in practice and may introduce artifacts, bias, or excessive noise, and such basis decompositions may require extensive calibration measurements and data preprocessing to obtain accurate results.

[0020] Due to the inherent complexity of many image reconstruction tasks, artificial intelligence (AI) and deep learning have begun to be used for general image reconstruction, with satisfactory results. It would be desirable to be able to use AI and deep learning for X-ray image processing tasks, including spectral CT. However, there is a general need for improved noise reduction methods in spectral CT.

[0021] Another current issue with deep learning image reconstruction is its limited explainability. An image may appear to have very low noise levels at first glance, but in fact contain errors due to biases in the neural network estimator. Explainable AI techniques would be able to provide some information about why an output image has certain characteristics, based on the input image and training data.

[0022] Another drawback of existing AI techniques is that they are generally not tunable, meaning that they can only provide a single output image for a given input image, with no possibility to adjust the characteristics of the output image without retraining the network.

[0023] Therefore, there is a need for improved denoising methods for spectral computed tomography (CT) in general, and denoising methods that are explainable and tunable in particular. overview

[0024] This Summary introduces concepts that are described in more detail in the Detailed Description. This Summary is not intended to identify essential features of the claimed subject matter, nor should it be used to limit the scope of the claimed subject matter. [Problem to be solved by the invention]

[0025] The inventors have realized that image reconstruction in spectral CT imaging is more challenging for two main reasons: 1) In addition to increased resolution, multiple bins and multiple materials in the analysis significantly increase the amount of data to be processed; and 2) efficient material decomposition and image reconstruction methods tend to produce noisy images that do not meet the expected image quality. Therefore, there is a need to denoise material images.

[0026] In this disclosure, a fast denoiser based on deep learning and linear minimum mean square error (LMMSE) is presented and combined in a model-based deep learning approach. This method incorporates prior knowledge into the denoiser while maintaining a linear estimator structure to provide interpretability of the results. The architecture, based on a linear estimator with matrices and vectors estimated by deep neural networks, offers significant flexibility over traditional deep learning denoisers.

[0027] This interpretability allows us to generate images with desired properties by adjusting the coefficients of the linear estimator. For example, we can increase or decrease one or more coefficients of the linear estimator to reduce large-area bias or improve the preservation of fine image details.

[0028] This adjustment can be done prior to image reconstruction, for example, during reconstruction method development, or it can be done in real time while the image is displayed to the end user, allowing the user to adjust the image to obtain desired image characteristics.

[0029] According to a first aspect, there is provided a method of denoising spectral CT image data, comprising determining a denoised linear estimate of the spectral CT image data by maximising or minimising a first objective function, wherein at least one parameter of the denoised linear estimate is determined by at least one machine learning system.

[0030] According to a second aspect, there is provided a CT imaging system comprising: an X-ray source configured to emit X-rays; an X-ray detector configured to generate spectral CT image data; and a processor configured to determine a denoised linear estimate of the generated spectral CT image data based on maximizing or minimizing a first objective function, wherein the processor is further configured to determine at least one parameter of the linear estimate by at least one machine learning system.

[0031] Various systems and methods for denoising spectral CT image data are provided, including determining a denoising linear estimate of the spectral CT image data by maximizing or minimizing a first objective function, where at least one parameter of the denoising linear estimate is determined by at least one machine learning system. The denoiser is based on a linear minimum mean square error (LMMSE) estimator. While LMMSE is very fast to compute, it is not commonly used for CT image denoising due to its inability to adapt the amount of denoising to different parts of the image and the difficulty of deriving accurate statistical properties from the CT image data. To overcome these issues, a model-based deep learning model, such as a deep neural network, that retains the model-based LMMSE structure is used. [Brief explanation of the drawings]

[0032] The present embodiments, together with further objects and advantages thereof, will best be understood by reference to the following description taken together with the accompanying drawings, in which: [Figure 1A] FIG. 1 is a schematic diagram illustrating an example of an X-ray imaging system. [Figure 1B] FIG. 1 is a schematic diagram illustrating an example of an X-ray imaging system. [Figure 2] FIG. 10 is a schematic diagram showing another example of an X-ray imaging device such as a CT imaging device. [Figure 3] 1 is a schematic block diagram of a CT imaging system as an example of an X-ray imaging system. [Figure 4] FIG. 10 is a schematic diagram showing another example of related parts of an X-ray imaging device such as a CT imaging device. [Figure 5] 1 is a schematic diagram of a photon counting circuit and / or device according to an exemplary embodiment. [Figure 6] FIG. 1 is a schematic diagram illustrating an example of a solid-state detector sub-module in accordance with an example embodiment. [Figure 7]FIG. 10 is a schematic diagram illustrating an example of a solid-state detector sub-module according to another exemplary embodiment. [Figure 8A] FIG. 10 is a schematic diagram illustrating an example of a solid-state detector sub-module according to yet another exemplary embodiment. [Figure 8B] FIG. 1 is a schematic diagram illustrating an example of a set of tiled detector sub-modules, each of which is a depth-separated detector sub-module, with an application specific integrated circuit (ASIC) or corresponding circuitry located below the detector sub-module when viewed from the direction of incident x-rays. [Figure 9] Schematic diagram of a conventional convolutional neural network (CNN)-based denoising technique, in which the CNN directly maps the noisy image to the clean image. [Figure 10] Schematic of the presented denoising technique, where a CNN is used to map the linear model parameters W and b, which are used to generate a clean image. [Figure 11] We demonstrate an example of the interpretability of the proposed model using three parameters σ, β, λ, which are used to control different components of the output image. [Figure 12] This shows an example of how the two components of a=WX+b can be interpreted in the results. [Figure 13] We demonstrate the parallelism of our approach with LMMSE. The first row shows the usual trained LMMSE (linear minimum mean square error) estimator components for a given phantom example, while the second row shows the equivalent estimator components of our trained approach. [Figure 14] FIG. 1 is a schematic diagram illustrating an example implementation of a computer according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0033] Next, embodiments of the present disclosure will be described by way of example with reference to the drawings.

[0034] For a better understanding, it will be useful to follow with an introductory description of a non-limiting example of an overall X-ray imaging system in which data processing and transfer in accordance with the concepts of the present invention may be implemented.

[0035] 2 is a schematic diagram illustrating an example of an X-ray imaging system 100, such as a CT imaging system, including an X-ray source 10 that emits X-rays, an X-ray detector 20 that includes an X-ray detector that detects X-rays that have passed through an object, an analog processing circuit 25 that processes and digitizes raw electrical signals from the X-ray detector, a digital processing circuit 40 that can perform further processing operations on the measurement data, such as applying corrections, temporarily storing, and filtering, and a computer 50 that can store the processed data and perform further post-processing and / or image reconstruction. The digital processing circuit 40 can include a digital processor. According to an exemplary embodiment, all or a portion of the analog processing circuit 25 can be implemented within the X-ray detector 20. The X-ray source and the X-ray detector can be coupled to a rotating member of a gantry 11 of the CT imaging system 100.

[0036] The entire X-ray detector may be considered an X-ray detector system 20, or an X-ray detector 20 combined with associated analog processing circuitry 25.

[0037] An image processing system 30, in communication with and electrically coupled to the analog processing circuit 25, may include a digital processing circuit 40 and / or a computer 50 and may be configured to perform image reconstruction based on image data from the x-ray detector. Thus, the image processing system 30 may be viewed as the computer 50, or a combined system of the digital processing circuit 40 and the computer 50, or as the digital processing circuit 40 alone, where the digital processing circuit is further specialized for image processing and / or reconstruction.

[0038] One example of a commonly used X-ray imaging system is a CT imaging system, which may include an X-ray source or tube that produces a fan or cone beam of X-rays and an opposing array of X-ray detectors that measure the percentage of the X-rays that pass through the patient or object. The X-ray source or tube and X-ray detectors are mounted on a gantry 11 that can rotate around the object to be imaged.

[0039] FIG. 3 shows a schematic diagram of a CT imaging system 100 as an example of an X-ray imaging system. The CT imaging system includes a computer 50 that receives commands and scanning parameters from an operator via an operator console 60, which may have a display 62 and some form of operator interface, such as a keyboard, mouse, joystick, touch screen, or other input device. The commands and parameters provided by the operator are then used by the computer 50 to provide control signals to an X-ray controller 41, a gantry controller 42, and a table controller 43. Specifically, the X-ray controller 41 provides power and timing signals to the X-ray source 10 to control the emission of X-rays to an object or patient residing on a table 12. The gantry controller 42 controls the rotational speed and position of the gantry 11, which comprises the X-ray source 10 and the X-ray detector 20. By way of example, the X-ray detector 20 may be a photon-counting X-ray detector. The table controller 43 controls and determines the position of the patient table 12 and the scan area of the patient. There is also a detector controller 44 configured to control and / or receive data from the x-ray detector 20 .

[0040] In an embodiment, computer 50 also performs post-processing and image reconstruction of image data output from x-ray detector 20. Computer 50 thereby corresponds to image processing system 30 as shown in Figures 1 and 2. An associated display 62 allows an operator to observe reconstructed images and other data from computer 50.

[0041] An X-ray source 10 disposed on a gantry 11 emits X-rays. An X-ray detector 20, which may be in the form of a photon-counting X-ray detector, detects the X-rays after they pass through an object or patient. The X-ray detector 20 is formed, for example, by a plurality of pixels, also called sensors or detector elements, and associated processing circuitry, such as an ASIC (Application Specific Integrated Circuit), disposed on a detector module. Some of the analog processing is implemented in the pixels, while the remaining processing is implemented, for example, in the ASIC. In one embodiment, the processing circuitry (ASIC) digitizes the analog signals from the pixels. The processing circuitry (ASIC) may also comprise digital processing that can perform further processing operations on the measurement data, such as applying corrections, temporary storage, and / or filtering. During a scan to acquire X-ray projection data, the gantry and the components mounted thereon rotate about an isocenter 13.

[0042] Modern X-ray detectors typically require the conversion of incident X-rays into electrons. This is usually achieved by the photoelectric effect or Compton interaction, and the resulting electrons typically produce secondary visible light until they lose energy, which is detected by a photosensitive material. Semiconductor-based detectors also exist, in which the electrons generated by the X-rays create charge electron-hole pairs that are collected by an applied electric field.

[0043] Detectors operating in energy integration mode exist in the sense that they provide a signal integrated from a large number of x-rays. The output signal is proportional to the total energy deposited by the detected x-rays.

[0044] Photon-counting and energy-resolved X-ray detectors are becoming increasingly common in medical X-ray applications. Photon-counting detectors have the advantage that they can, in principle, measure the energy of each X-ray, providing additional information about the composition of the object being examined. This information can be used to improve image quality and reduce radiation dose.

[0045] Typically, photon-counting X-ray detectors determine the energy of a photon by comparing the height of the electrical pulse generated by the photon's interaction within the detector material to a series of comparator voltages. These comparator voltages are also called energy thresholds. The analog voltages of the comparators are typically set by a digital-to-analog converter (DAC). The DAC converts the digital settings sent from the controller into analog voltages against which the height of the photon pulse can be compared.

[0046] Photon-counting detectors count the number of photons that interact within the detector during a measurement period. A new photon is typically identified by an electrical pulse whose height exceeds the comparator voltage of at least one comparator. Once a photon is identified, the event is stored by incrementing a digital counter associated with the channel.

[0047] Using multiple different thresholds results in an energy-discriminating photon counting detector that can sort detected photons into energy bins corresponding to the various thresholds. This type of photon counting detector is sometimes called a multi-bin detector. Generally, energy information allows for the creation of new types of images, where new information is available and image artifacts inherent in conventional techniques can be eliminated. In other words, in an energy-discriminating photon counting detector, the pulse height is compared to a number N of programmable thresholds (T1-TN) in a comparator, and the photon counts are sorted according to their pulse height, which is proportional to their energy. In other words, a photon counting detector that includes more than one comparator is called a multi-bin photon counting detector. In a multi-bin photon counting detector, photon counts are typically stored in a set of counters, one for each energy threshold. For example, one count can be assigned to the highest energy threshold exceeded by a photon pulse. In another example, a counter records the number of times a photon pulse exceeds each energy threshold.

[0048] As an example, edge-on is a special, non-limiting design for photon-counting detectors in which the x-ray sensors, such as x-ray detecting elements or pixels, are oriented edge-on with respect to the incident x-rays.

[0049] For example, such a photon counting detector can have pixels in at least two directions, one of which has a component in the direction of the X-ray. Such an edge-on photon counting detector may also be referred to as a depth-segment photon counting detector, having pixels in two or more depth segments in the direction of the incident X-ray. It should be noted that one detector element may correspond to one pixel, and / or multiple detector elements may correspond to one pixel, and / or data signals from multiple detector elements may be used for one pixel.

[0050] Alternatively, the pixels may be arranged as an array (non-depth-segmented) in a direction substantially perpendicular to the direction of the incident X-rays, and each of the pixels may be oriented edge-on with respect to the incident X-rays. In other words, the photon-counting detector may be non-depth-segmented while still being positioned edge-on with respect to the incident X-rays.

[0051] By arranging the edge-on photon counting detector edge-on, the absorption efficiency can be increased, in which case the absorption depth can be chosen to be any length, and the edge-on photon counting detector can be fully depleted without requiring very high voltages.

[0052] The conventional mechanism for detecting X-ray photons directly through semiconductor detectors basically works as follows: the energy of the X-ray interaction in the detector material is converted into electron-hole pairs inside the semiconductor detector, and the number of electron-hole pairs is generally proportional to the photon energy. The electrons and holes drift towards the electrodes and backside of the detector (or vice versa). During this drift, the electrons and holes induce a current in the electrodes, and this current can be measured.

[0053] As shown in FIG. 4 , signals are routed via routing paths 26 from detector elements 22 of the X-ray detector to inputs of analog processing circuitry (e.g., ASIC) 25. It should be understood that the term Application Specific Integrated Circuit (ASIC) is broadly interpreted as a general circuit used and configured for a specific application. The ASIC processes the electrical charge generated from each X-ray and converts it into digital data that can be used to obtain measurement data such as photon count and / or estimated energy. The ASIC is configured to interface with the digital processing circuitry so that the digital data is sent to digital processing circuitry 40 and / or one or more memory circuits or components 45, and ultimately, the data is input to image processing circuitry 30 of FIG. 2 or computer 50 to generate a reconstructed image.

[0054] Since the number of electrons and holes generated by an X-ray event is proportional to the energy of the X-ray photon, the total charge contained in one induced current pulse is proportional to this energy. After a filtering step in the ASIC, the pulse amplitude is proportional to the total charge of the current pulse and therefore to the X-ray energy. The pulse amplitude can be measured by comparing its value with one or more thresholds (THR) in one or more comparators (COMP), and a counter is introduced to record the number of times the pulse is greater than the threshold. In this way, it is possible to count and / or record the number of X-ray photons detected within a certain time period with energies exceeding the respective thresholds (THR).

[0055] The ASIC typically samples the analog photon pulse once per clock cycle and records the output of a comparator. The comparators (threshold) output a 1 or 0 depending on whether the analog signal was above or below the comparator voltage. The information available with each sample is, for example, a 1 or 0 for each comparator representing whether the comparator was triggered (the photon pulse was above the threshold) or not.

[0056] In a photon counting detector, there is typically photon counting logic that determines if a new photon has been recorded and records the photon in a counter. In a multi-bin photon counting detector, there are typically multiple counters, for example, one for each comparator, and the photon count is recorded in the counter according to an estimate of the photon energy. The logic can be implemented in several different ways. Two of the most common categories of photon counting logic are non-paralyzable counting modes and paralyzable counting modes. Other photon counting logic includes, for example, local maximum detection, which counts detected local maxima in a voltage pulse and sometimes records the pulse height.

[0057] Photon-counting detectors have many advantages, including but not limited to high spatial resolution, low sensitivity to electronic noise, excellent energy resolution, and material separation capabilities (spectral imaging capabilities). However, energy-integrating detectors have the advantage of high count-rate tolerance. Count-rate tolerance comes from the fact / realization that because the total energy of the photons is measured, adding one additional photon will always (within a reasonable range) increase the output signal, regardless of the amount of photons currently registered by the detector. This advantage is one of the main reasons why energy-integrating detectors have become the standard in medical CT today.

[0058] FIG. 5 is a schematic diagram of a photon counting circuit and / or device according to an exemplary embodiment.

[0059] When a photon interacts in the semiconductor material, a cloud of electron-hole pairs is generated. When an electric field is applied to the detector material, the charge carriers are collected at electrodes attached to the detector material. A signal is sent from the detector element to the input of a parallel processing circuit, such as an ASIC. In one example, the ASIC can process the charge in such a way that a voltage pulse is generated whose maximum height is proportional to the amount of photon energy deposited in the detector material.

[0060] The ASIC may include a set of comparators 302, each of which compares the magnitude of the voltage pulse with a reference voltage. The comparator output is typically either zero or one (0 / 1), depending on which of the two compared voltages is greater. Here, we assume that the comparator output is one if the voltage pulse is higher than the reference voltage, and zero if the reference voltage is higher than the voltage pulse. A digital-to-analog converter (DAC) 301 may be used to convert a digital setting, which may be provided by a user or a control program, into a reference voltage that may be used by the comparators 302. If the height of the voltage pulse exceeds the reference voltage for a particular comparator, that comparator is said to be triggered. Each comparator is typically associated with a digital counter 303, which is incremented based on the comparator output according to photon-counting logic.

[0061] As mentioned above, the estimated

number

[0062] It will be understood that the features and arrangements described herein can be implemented, combined and rearranged in various ways.

[0063] For example, embodiments may be implemented in hardware, or at least partially in software for execution by suitable processing circuitry, or a combination thereof.

[0064] The steps, functions, procedures, and / or blocks described herein may be implemented in hardware using conventional techniques, including both general-purpose electronic circuitry and application-specific circuitry, such as discrete or integrated circuit technology.

[0065] Alternatively, or as a complement, at least some of the steps, functions, procedures and / or blocks described herein may be implemented in software, such as a computer program, for execution by suitable processing circuitry, such as one or more processors or processing units.

[0066] Non-limiting examples of specific detector modules are described below. More specifically, these examples refer to edge-on directional detector modules and depth-resolved detector modules. Other types of detectors and detector modules may also be possible.

[0067] 6 is a schematic diagram illustrating an example of a semiconductor detector sub-module according to an exemplary embodiment. This is an example of a detector module 21 with a semiconductor sensor having a plurality of detector elements or pixels 22, each of which typically consists primarily of a diode with a charge collection electrode. X-rays enter the detector module from the end.

[0068] 7 is a schematic diagram showing an example of a semiconductor detector sub-module according to another exemplary embodiment, in which a detector module 21 having a semiconductor sensor is also divided into a plurality of depth segments or detector elements 22 in the depth direction, assuming that X-rays are incident from the end of the detector module.

[0069] A detector element is typically an individual X-ray sensitive sub-element of a detector. Generally, photon interactions occur within a detector element, and the charge thus generated is collected on a corresponding electrode of the detector element.

[0070] Each detector element typically measures the incident X-ray flux as a sequence of frames, where a frame is a specified time interval called the frame time.

[0071] Depending on the detector topology, a detector element may correspond to a pixel, particularly if the detector is a flat panel detector. A depth-segmented detector may be considered to have multiple detector strips, each strip having multiple depth segments. In such a depth-segmented detector, each depth segment may be considered to be a separate detector element, particularly if each depth segment is associated with its own separate charge collection electrode.

[0072] The detector strips in a depth-segmented detector usually correspond to the pixels in a regular flat panel detector, and are therefore sometimes called pixel strips, but a depth-segmented detector can also be thought of as a 3D pixel array, where each pixel corresponds to an individual depth segment / detector element.

[0073] Semiconductor sensors can be implemented as so-called multi-chip modules (MCMs), using the semiconductor sensor as a base substrate for electrical wiring and multiple ASICs, preferably attached by flip-chip technology. The wiring includes connections for signals from each pixel or detector element to the ASIC inputs and connections from the ASIC to external memory and / or digital data processing. Power to the ASIC can be provided through similar wiring, taking into account the increased cross-sectional area required for the high currents in these connections, but power can also be provided through a separate connection. ASICs can be placed on the sides of the active sensor. This means that an absorbing cover can be placed on top to protect against incident X-rays, and an absorber can be placed in this direction to protect against scattered X-rays from the side.

[0074] Figure 8A is a schematic diagram showing a detector module implemented as an MCM similar to the embodiment of U.S. Patent No. 8,183,535. In this example, it is shown that a semiconductor sensor 21 can also function as a substrate within the MCM. Signals are routed by wiring paths 23 from the detector elements 22 to the inputs of a parallel processing circuit 24 (e.g., an ASIC) located next to the active sensor area. The ASIC processes the electrical charge generated from each X-ray and converts it into digital data that can be used to detect photons and / or estimate their energy. The ASIC can have its own digital processing circuitry and memory for small tasks. The ASIC can then be configured to connect to digital processing and / or memory circuits or components located outside the MCM, and the data is ultimately used as input for reconstructing an image.

[0075] However, the adoption of depth segments poses two significant challenges for silicon-based photon-counting detectors. First, a large number of ASIC channels must be employed to process the data provided by the associated detector segments. In addition to the increased channel count due to the reduced pixel size and depth segmentation, multi-energy bins further increase data size. Second, because a given X-ray input count is divided into smaller pixels, segments, and energy bins, the signal in each bin is very low, and detector calibration / correction requires calibration data of several orders of magnitude or more to minimize statistical uncertainty.

[0076] Naturally, increasing data size by several orders of magnitude requires more computing resources, such as hard disks, memory, central processing units (CPUs) or graphics processing units (GPUs), and slows down both data processing and preprocessing. For example, increasing data size from 10 megabytes to 10 gigabytes can increase the time required to read and write data by a factor of 1000.

[0077] A problem with counting-type X-ray photon detectors is the pile-up problem. At high X-ray photon flux rates, there can be problems distinguishing between two successive charge pulses. As mentioned above, the pulse length after filtering depends on the shaping time. If this pulse length is greater than the time between two X-ray photon-induced charge pulses, the pulses grow together, and the two photons become indistinguishable and may be counted as a single pulse. This is called pile-up. Therefore, one way to avoid pile-up at high photon flux is to use a short shaping time or to use depth segmentation.

[0078] For pile-up calibration vector generation, pile-up calibration data must be preprocessed for spit correction. For material decomposition vector generation, material decomposition data should preferably be preprocessed for both spit and pile-up correction. For patient scan data, preprocessing for spit, pile-up, and material decomposition is required before image reconstruction. These are simplified examples to illustrate "preprocessing," as the actual preprocessing steps can include several other calibration steps, such as reference normalization and air calibration, as needed. The term "processing" can sometimes refer only to the final step in each calibration vector generation or patient scan, but is sometimes used interchangeably.

[0079] FIG. 8B is a schematic diagram illustrating an example of a set of tiled detector sub-modules, each of which is a depth-segmented detector sub-module, with ASICs or corresponding circuitry 24 positioned below the detector elements 22 as viewed from the direction of incident x-rays, allowing routing paths 23 from the detector elements 22 to parallel processing circuitry 24 (e.g., ASICs) in the spaces between the detector elements.

[0080] Artificial intelligence (AI) and deep learning have begun to be used for general image reconstruction, and some satisfactory results have been obtained. However, a current problem with deep learning image reconstruction is its limited explainability. Even if an image appears to have a very low noise level, it actually contains errors due to the bias of the neural network estimator.

[0081] In general, deep learning refers to machine learning techniques using representation learning based on artificial neural networks and similar architectures. Learning can be supervised, semi-supervised, or unsupervised. Deep learning systems, such as deep neural networks, deep belief networks, recurrent neural networks, and convolutional neural networks, have been applied to a variety of technology fields, including computer vision, speech recognition, natural language processing, social network filtering, machine translation, and board game programs, producing results that rival and in some cases exceed the performance of human experts.

[0082] The adjective "deep" in deep learning comes from the use of multiple layers in the network. Early work showed that linear perceptrons could not be universal classifiers, and that networks with non-polynomial activation functions and a single hidden layer of unlimited width could be universal classifiers. Deep learning is a modern variation, involving unlimited layers, enabling practical applications and optimized implementations. In deep learning, for efficiency, ease of learning, and understandability, layers are heterogeneous and allowed to deviate significantly from biologically informed connectionist models.

[0083] The present inventors have recognized that there is a need for denoising algorithms with improved performance for spectral CT, particularly algorithms with improved interpretability.

[0084] The proposed technique is generally applicable to providing denoised image data in spectral CT based on neural networks and / or deep learning.

[0085] To provide an exemplary framework to facilitate understanding of the proposed technique, we next present a concrete example of deep learning-based image reconstruction in the specific context of spectral CT image reconstruction.

[0086] However, it should be understood that the proposed technique for providing an indication of the reliability of deep learning-based image reconstruction in spectral CT applications is generally applicable to deep learning-based image reconstruction for CT and is not limited to the following specific example of deep learning-based image reconstruction.

[0087] We present a novel and fast denoiser based on the Linear Minimum Mean Square Error (LMMSE) estimator. Although LMMSE is computationally very fast, it has not been commonly used for CT image denoising, likely due to the inability to adapt the amount of denoising to different parts of the image and the difficulty of deriving accurate statistical characteristics from CT data. To overcome these issues, we propose a model-based deep learning strategy, i.e., a deep neural network (model-based) that preserves the LMMSE structure. In this way, the solution adapts to the anatomical structure at each point in the image and the noise characteristics at that specific location.

[0088] As an exemplary and non-limiting embodiment of the present disclosure, consider the linear minimum mean square error (LMMSE) for denoising two material images after FPB, i.e., x=[x1, x2], which is the solution:

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[0090] Let us explain how we think about model-based deep learning in this scenario. We have a model-based solution (LMMSE denoiser), but if we use only diagonal cross- and co-covariances, we need to enhance the model-based solution (LMMSE denoiser) to obtain good estimates of W and b. Therefore, we want to preserve the mathematical structure (linear, fast) by using deep learning inference (a powerful statistical, model-independent approach to estimate the LMMSE parameters). Enforcing a problem structure leads to a neural network that requires fewer training samples and is more robust to unknown datasets than typical "black-box" networks. Of course, we also expect the results to be much better than the oversimplified LMMSE approach, which considers diagonal cross- and co-covariances. Our deep learning solution is shown in Figure 10.

[0091] There is a further interpretation of this result: the goal of this network is not to obtain a denoised image, but to obtain W and b. Therefore, if we want to manipulate and understand the solution, instead of changing or accessing millions of parameters inside the CNN, we can consider the W and B parameters, which are considerably fewer and also more “interpretable” (in connection to an LMMSE).

[0092] The proposed deep learning approach requires a training database. To demonstrate the proof-of-concept of the proposed disclosure, we trained a trained LMMSE estimator using simulated photon-counting data. PCCT measurements are calculated using an 8-bin silicon detector, and then two material decompositions and FBP are performed to obtain material images. We simulated a set of 1,200 cases. We used the KiTS19 database, which primarily consists of abdominal scans. We used 1,000 samples for training and 200 samples for testing. To evaluate the robustness of our technique in adapting to unseen data, we also simulated 200 additional scans from another database (NSCLS). This database also contains whole-body scans, providing greater anatomical diversity than the training database.

[0093] In this example, we use PyTorch and one NVIDIA GPU GeForce RTX 2080 Ti GPU board to train the neural network. To perform a comparative study, we consider the following competing solutions: (1) the original simplified LMMSE as described in the previous section, and (2) a "black-box" CNN based on the UNet architecture.

[0094] FIG. 9 shows a schematic of a conventional CNN-based denoising technique 90, in which a black-box CNN 94 directly maps from a noisy CT image 92 to a clean CT image 96.

[0095] Figure 10 shows an overview of the proposed denoising technique 1000, in which a CNN 1004 accepts a noisy CT image 1002 as input, the CNN finds a linear estimator 1004, the CNN is used to map linear model parameters W and b, and the linear estimator is used to perform denoising 1006 and generate a clean CT image. Thus, a linear structure is enforced in the learning process.

[0096] Figure 11 shows an example of this interpretability. The learned linear components W and b can be manipulated with a few parameters. ii ("variance" of single material component of the linear model), w ij Three parameters, σ, β, and λ, are used to control σ (the “cross-covariance” of opposite material component), b (the mean or “bias” of single material component). When the bias is zero (λ=0), the results show enhanced structure. ij If is zero (β=0) 10, cross-contamination between materials is not significantly corrected. Furthermore, if the "variance" component is zero (σ=0) 10, it can be the single material noise variance that is not reduced.

[0097] Figure 12 shows a=W x Here is an example of how the two components of +b affect the result: x) provides anatomical details (finer edges, localized small structures) as shown in CT image 1016 (structure image), but does not provide the exact CT number expressed in Hounsfield Units (HU). The second independent term, b, generally corrects the HU value (mean, or bias) resulting in little anatomical details (a very smoothed image), as shown in CT image 1018 (bias image).

[0098] Figure 13 shows an empirical demonstration of the parallelism of our technique with LMMSE. The first row 1020 shows the estimator components of the regular LMMSE for a particular phantom example, and the second row 1030 shows the equivalent estimator components of our learned approach. We can see that LMMSE is not specific enough, and the results are too blurry to accurately represent the denoised example. However, our approach is more specific and accurate while still retaining similarity to the LMMSE described above. Therefore, this can be interpreted as DNN-enhanced LMMSE (which is the best linear estimator to minimize MSE).

[0099] The present disclosure relates to spectral or energy-resolved image data consisting of image data including at least two spectral components. In this context, image data can be, for example, two-dimensional, three-dimensional, or time-resolved, and refers to either a reconstructed image or an intermediate representation of the image data, such as a sinogram. The different spectral components can be, for example, a composite mono-energy image, a wide-spectrum image acquired at different tube acceleration voltages, or a material-selective image such as a basis image. The different spectral components can also be a combination of the above.

[0100] The above description should be understood as illustrative and non-limiting, and several variations of the described method are possible. For example, several different architectures of convolutional neural networks are possible, such as UNet, ResNet, or an unrolled iterative network, e.g., an unrolled gradient descent or unrolled primal-dual network. Furthermore, different pooling layers, such as batch normalization, skip connections, and maximum, average, or softmax pooling, may or may not be desirable during network training. Various loss functions may be minimized during network training, such as L1 loss, L2 loss, perceptual loss, and adversarial loss. Perceptual losses can be implemented using different classifier networks, and different layers of such networks can be used to capture different image characteristics.

[0101] We consider that taking W as a complete matrix and using a neural network to obtain all its elements is 10 12We recognize that this is impractical, as it would require a neural network with an output of approximately . Therefore, it is desirable to impose some structure on the matrix, for example, by making W a sparse matrix, i.e., a matrix with a small number of non-zero elements. For example, the matrix W can be diagonal, in which case, when the matrix is applied, each pixel value in the image data set is multiplied by a value. Another option is to make W a block-diagonal matrix. For example, if the spectral data consists of N spectral components, W consists of NxN blocks of elements along the diagonal, and applying W to the vector transforms the values corresponding to the different spectral components of a particular pixel by the NxN blocks, resulting in a new set of spectral components for the corresponding transformed spectral component image set.

[0102] As another example, W can be made to operate separately on each of the different spectral components, with entries corresponding to crosstalk between the different components set to zero. In both the case where W operates separately on each of the different spectral components, and the more general case where W includes entries for the corresponding cross-components, it can be thought of as corresponding to some maximum distance in pixels between the input pixel and the output pixel. Alternatively, W can be considered in the Fourier domain as W=F -1 W F It can be expressed as a transformation in F, where F is the Fourier transform operator, and W corresponds to specific frequencies such as low and high frequencies. F Only the elements of are non-zero.

[0103] Another example is to let W be an element of the range of a linear or nonlinear transformation, such as an artificial or convolutional neural network.

[0104] The vector b can also be selected as, for example, a full vector without any restrictions or a sparse vector where only certain elements are nonzero. In another exemplary embodiment of the present disclosure, b can be restricted to the range of a linear or nonlinear transformation, such as an artificial or convolutional neural network, or a linear combination of Fourier components b=F -1 b F can be limited to, where b F is a vector of Fourier components of b that can for example be restricted to contain high or low spatial frequencies.

[0105] In practice, imposing such constraints on W and B can be done by having the convolutional neural network output only those elements of W and b that should be non-zero, and setting the other components to zero. In another embodiment of the present disclosure, the convolutional neural network can generate feature vectors that are subsequently transformed from W and b, for example, via a linear transformation or via an artificial or convolutional neural network.

[0106] For example, a neural network can generate multiple Fourier components and transform them to form, for example, one or more diagonals of b or W. In another embodiment of the present disclosure, different components of b and / or W, or feature vectors associated with b and / or W, are given different weights in the loss function used to train the neural network to generate these components, or are penalized by a penalty term to make these components less likely to achieve large values. For example, the components of b and / or W can be normalized so that high spatial frequencies are penalized, meaning that these components contain primarily low frequencies. In this way, excessive variation between transformations applied to neighboring pixels can be avoided, making the denoising method more robust to differences in noise characteristics and image appearance compared to the training dataset. In another example, low frequencies can be penalized, providing a denoising device that is particularly well-suited to preserving fine details.

[0107] We appreciate that the linear structure of our denoiser provides both explainability and tunability. The trained LMMSE denoiser has a similar mathematical structure to conventional LMMSE denoisers based on handcrafted noise models. Comparing the coefficients of the trained LMMSE denoiser with those of conventional LMMSE denoisers can provide information about how the denoiser behaves on an image. For example, such a comparison can show that the behavior of the trained LMMSE denoiser in a limited region of an image is similar to that of a conventional LMMSE denoiser built based on a specific model of the signal and noise. This information can be useful for analyzing image quality and robustness characteristics and for improving the trained LMMSE denoiser by, for example, adjusting the structure and training parameters of b and / or W.

[0108] The structure of the linear LMMSE denoiser also allows for tuning of the model, e.g.

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[0109] Such manipulation of coefficients can be achieved by multiplying a selected set of coefficients by a constant factor, or

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[0110] As an example, the inventors

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[0111] In another embodiment of the present disclosure, the tunability is achieved by training a single neural network based on the tuning parameter t.

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[0112] In another example, t can be replaced by multiple adjustment parameters to adjust several different characteristics of the image.

[0113] In yet another embodiment of the present disclosure, real-time adjustability can be achieved while the image is being displayed to the end user, allowing the user to adjust the image to achieve desired image characteristics.

[0114] In an exemplary embodiment of the present disclosure, the convolutional neural network is trained by minimizing an L1 loss function, an L2 loss function, a perceptual loss function, an adversarial loss function, or a combination thereof.

[0115] The goal of the network is to find a=W for a=[a1,a2]. x +b, and the denoised image corresponds to the material image x = [x1, x2]. Here we will discuss the case of two spectral components, but this is a non-limiting example, and the vectors a and x can in general have any number of components greater than or equal to two. The goal is to

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[0116] One possible solution is to use a feature-based perceptual loss, which compares feature representations corresponding to the output and ground truth instead of comparing the output and ground truth pixel by pixel. The feature representations are obtained by passing the target and output through a pre-trained convolutional neural network (CNN). For example, VGG16 / 19 (a CNN from the Visual Geometry Group at the University of Oxford) is often used as a feature extractor. This perceptual loss is used in various computer vision problems, such as image denoising and super-resolution. If we denote the j-th layer of a pre-trained CNN by φj, the perceptual loss is given by

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[0117] Another possibility is to minimize some notion of distance between the ground truth and the distribution of output images. This can be achieved using an adversarial loss based on generative adversarial networks (GANs). In this setting, the network is pitted against another CNN in a minimax game, with incremental improvements making the output distribution indistinguishable from the ground truth distribution. This avoids the over-denoising and over-smoothing that comes with pixel-wise losses like L2 and L1 losses.

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[0118] For an optimal discriminator, the generator's objective is

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[0119] While WGAN-GP is not necessarily the best-performing GAN, it is one of the most stable GANs for training. Previous publications have demonstrated the stability of WGAN-GP across several different tasks and datasets without experiencing common problems such as vanishing gradients and mode collapse.

[0120] To trade off the advantages and disadvantages of these loss functions, we can consider a weighted sum of the loss functions mentioned above.

[0121] In an exemplary embodiment of the present disclosure, the convolutional neural network is trained as part of a pair of cycle-consistent generative adversarial networks (cycle GANs).

[0122] The data required for this study are paired samples of noisy material images and their ground truth (low-noise) counterparts. However, in many cases, such paired datasets are unavailable. Instead, we might have a pile of noisy material images and a pile of denoised / low-noise material images. To extend the learned LMMSE to unpaired data, we apply so-called cycle-consistent GANs. The key insight that makes this possible is cycle-consistent loss. The objective is to find a map from a source domain X (X) to a target domain A. Let G:X->A be the map that takes a pair of noisy material images x, passes it through our network, and forms a denoised material image a = Wx + b. Using an adversarial loss, we can push the distribution induced by G(X) such that it is indistinguishable from that of A. However, this mapping is highly constrained and the space of possible mappings is huge. To reduce the space of possible mappings, we can consider the inverse mapping F:A->X and enforce cycle consistency with a cycle-consistent loss. This mapping is

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[0123] This means that each has its own unique discriminator D A and D X It is combined with a GAN for mapping G and inverse mapping F, with

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[0124] Like the original GAN, this formulation suffers from training stability issues. To circumvent this, the negative log likelihood loss is replaced by an L2 loss. In other words, the generator

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[0125] The method proposed by the present inventors includes the steps of: (1) acquiring energy-resolved CT image data;

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[0126] In an exemplary embodiment of the present disclosure,

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[0127] In exemplary embodiments of the present disclosure, the image quality measures are a mean-squared error, structural similarity, bias, fidelity of fine details, numerical observer detectability, visual grading score or observer performance.

[0128] In an exemplary embodiment of the present disclosure,

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[0129] In another exemplary embodiment of the present disclosure,

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[0130] In another exemplary embodiment of the present disclosure,

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[0131] In an exemplary embodiment of the present disclosure, the convolutional neural network has a ResNet architecture, a UNet architecture, an unrolled iterative architecture, or a combination thereof.

[0132] In an exemplary embodiment of the present disclosure, the convolutional neural network is trained by minimizing an L1 loss function, an L2 loss function, a perceptual loss function, an adversarial loss function, or a combination thereof.

[0133] In an exemplary embodiment of the present disclosure, a convolutional neural network is trained as a generator of a generative adversarial network.

[0134] In an exemplary embodiment of the present disclosure, the convolutional neural network is trained as part of a pair of cycle-consistent generative adversarial networks (cycle GANs).

[0135] In an exemplary embodiment of the present disclosure, the energy-resolved image data x is a set of sinograms.

[0136] In another exemplary embodiment of the present disclosure, the energy-resolved image data x is a set of reconstructed images.

[0137] In exemplary embodiments of the present disclosure, different components of the energy-resolved image data x consist of monoenergetic image data at different monochromatic energies, or image data corresponding to different measured energy levels or energy bins, or different basis images.

[0138] In an exemplary embodiment of the present disclosure, an end user:

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[0139] In another exemplary embodiment of the present disclosure, a convolutional neural network is trained on a dataset including a plurality of low-noise images having different image characteristics for each high-noise image, and the neural network is trained to generate low-noise images with different characteristics for each setting of at least one tuning parameter.

[0140] 14 is a schematic diagram illustrating an example of a computer implementation according to an embodiment. In this particular example, system 200 includes a processor 210 and a memory 220, where the memory includes instructions executable by the processor, thereby enabling the processor to perform the steps and / or actions described herein. The instructions are typically configured as computer programs 225, 235 and may be pre-configured in memory 220 or downloaded from an external memory device 230. Optionally, system 200 includes an input / output interface 240 interconnected to one or more processors 210 and / or memory 220 and may allow input and / or output of relevant data, such as one or more input parameters and / or one or more resulting output parameters.

[0141] The term "processor" should be construed in a general sense as any system or device capable of executing program code or computer program instructions to perform specific processing, decision-making, or computational tasks.

[0142] Thus, processing circuitry, including one or more processors, is configured, when executing a computer program, to perform well-defined processing tasks as described herein.

[0143] The processing circuitry need not be specialized solely in performing the steps, functions, procedures and / or blocks described above, but may also perform other tasks.

[0144] The present technology also provides a computer program product comprising a computer readable medium 220, 230 having such a computer program stored thereon.

[0145] As an example, the software or computer program 225, 235 can be implemented as a computer program product, which is typically carried or stored on a computer-readable medium 220, 230, particularly a non-volatile medium. The computer-readable medium can include one or more removable or non-removable memory devices, including, but not limited to, read-only memory (ROM), random-access memory (RAM), compact discs (CDs), digital versatile discs (DVDs), Blu-ray discs, universal serial bus (USB) memory, hard disk drive (HDD) storage, flash memory, magnetic tape, or any other conventional memory device. Thus, the computer program can be loaded into the operating memory of a computer or equivalent processing device for execution by its processing circuitry.

[0146] Thus, the computer programs resident in the memory can be organized as appropriate functional modules configured to perform at least some of the steps and / or tasks described herein when executed by the processor.

[0147] As mentioned above, at least some of the steps, functions, procedures, and / or blocks described herein may be implemented in software, such as a computer program, for execution by suitable processing circuitry, such as one or more processors or processing units.

[0148] When a processing procedure is executed by one or more processors, it can be considered as a computer action flow. The corresponding device, system, and / or apparatus can be defined as a group of functional modules, and each step executed by the processor corresponds to a functional module. In this case, the functional module is implemented as a computer program executed on the processor. Therefore, the device, system, and / or apparatus may alternatively be defined as a group of functional modules, and the functional module is implemented as a computer program executed on at least one processor.

[0149] Thus, the computer programs resident in the memory can be organized as appropriate functional modules configured to perform at least some of the steps and / or tasks described herein when executed by the processor.

[0150] Alternatively, most of the modules can be implemented as hardware modules or alternatively implemented in hardware - software or hardware is purely an implementation choice.

[0151] As used herein, elements or steps described in the singular and preceded by the word "a" or "an" should be understood not to exclude a plural of the elements or steps, unless such exclusion is expressly stated. Furthermore, references to "one embodiment" of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the referenced features. Furthermore, unless expressly stated to the contrary, embodiments that "comprise," "include," or "have" an element or elements having a particular characteristic may include additional such elements that do not possess that characteristic. The terms "comprise" and "have" are used as plain-language equivalents of the terms "comprise" and "possess," respectively. Furthermore, terms such as "first," "second," and "third" are used merely as labels and are not intended to impose numerical requirements or a particular positional order on their objects.

[0152] The embodiments of the present disclosure illustrated in the drawings and described above are merely exemplary embodiments and are not intended to limit the scope of the appended claims, including equivalents as may be included therein. Those skilled in the art will understand that various modifications, combinations, and variations can be made to the embodiments without departing from the scope defined by the appended claims. Any combination of non-mutually exclusive features described herein is intended to be within the scope of the present invention. That is, features of the described embodiments may be combined with any appropriate aspect described above, and any feature of any one aspect may be combined with any other appropriate aspect. Similarly, features described in a dependent claim may be combined with non-mutually exclusive features of other dependent claims, particularly if the dependent claims depend on the same independent claim. In some jurisdictions, single dependent claims may be used because such practice requires it, but this does not mean that the features of the dependent claims are mutually exclusive.

[0153] Furthermore, it should be noted that the inventive concept relates to all possible combinations of features unless expressly stated otherwise, in particular different component solutions in the different embodiments can be combined in other configurations, if technically possible. [Explanation of symbols]

[0154] 10: X-ray source 11: Gantry 12: Table 13: Isocenter 20: X-ray detector 21, 22: X-ray detector element / pixel / detector module / semiconductor sensor 23: Path 24: Parallel processing circuit 25: Analog processing circuit 26: Path 30: Image processing system 40: Digital processing circuit 41: X-ray control device 42: Gantry control device 43: Table control device 44: Detector control device 45: Memory 50: Computer 30: Image processing system 40: Digital processing circuit 41: X-ray control device 42: Gantry control device 43: Table control device 44: Detector control device 45: Memory 50: Computer 60: Operator console 62: Display 90, 1000: Noise reduction technology 92: Noisy CT image 94: Black box CNN 96: Clean CT image 100: X-ray imaging system 200: System 210: Processor 220: Memory / computer readable medium 225, 235: Computer program 230: External memory device / computer readable medium 240: Input / output interface 301: Digital-to-analog converter (DAC) 302: Comparator 303: Digital counter 1002: Noisy CT image 1004: CNN 1006: Noise removal 1010: Bias is zero 1012: "Cross-covariance" wij is zero 1014: "Variance" component is zero 1016: Structural image 1018: Bias image

Claims

1. 1. A method for denoising spectral CT image data, comprising:

1. A method comprising determining a denoised linear estimate of spectral CT image data by maximizing or minimizing a first objective function, wherein at least one parameter of the denoised linear estimate is determined by at least one machine learning system.

2. Determining the denoised linear estimate of the spectral CT image data includes: receiving spectral CT image data; processing the spectral CT image data based on the at least one machine learning system to obtain a matrix W and a vector b; forming denoised spectral CT image data a according to linear estimation according to a=WX+b; 10. The method of claim 1, wherein x is a representation of spectral CT image data comprising at least two spectral components.

3. 3. The method of claim 2, wherein at least one of the matrix W and the vector b is adjustable to optimize at least one image quality metric of the CT image data by maximizing or minimizing the first objective function.

4. 3. The method of claim 2, wherein the first objective function is at least one of mean squared error, structural similarity, bias, fine detail fidelity, numerical observer detectability, visual rating, and observer performance.

5. The method of claim 2 , wherein the matrix W is a diagonal matrix.

6. 3. The method of claim 2, wherein the matrix W is a block diagonal matrix, and non-zero off-diagonal entries of the matrix W correspond to cross terms between the at least two spectral components at each pixel of the spectral CT image data.

7. The method of claim 2 , wherein the matrix W is a sparse matrix, and non-zero elements of the matrix W correspond to pixels of the spectral CT image data that are located adjacent to each other.

8. 3. The method of claim 2, wherein the at least one machine learning system is trained by minimizing at least one of an L1 loss function, an L2 loss function, a perceptual loss function, and an adversarial loss function.

9. The method of claim 2 , wherein the spectral CT image data x comprises at least one of a set of sinograms and a set of reconstructed CT images.

10. 3. The method of claim 2, wherein the at least two spectral components of the spectral CT image data x include at least one of monochromatic image data at different monochromatic energies, image data corresponding to different measurement energy levels or energy bins, and different basis images.

11. The method of claim 2 , wherein at least one of the matrix W and the vector b of the denoised spectral CT image data a is adjusted by an end user.

12. The method of claim 2 , wherein the at least one machine learning system comprises at least one convolutional neural network (CNN).

13. 13. The method of claim 12, wherein the at least one convolutional neural network comprises at least one of a ResNet architecture, a UNet architecture, and an unrolled iterative architecture.

14. 13. The method of claim 12, wherein the at least one convolutional neural network is trained as a generator of a generative adversarial network (GAN).

15. 13. The method of claim 12, wherein the at least one convolutional neural network is trained as part of a pair of cycle-matched generative adversarial networks (GANs).

16. 13. The method of claim 12, wherein the at least one convolutional neural network is trained on a dataset including a plurality of low-noise images having different image characteristics for each high-noise image, and is trained to generate low-noise images with different characteristics for each setting of at least one tuning parameter.

17. 1. A CT imaging system, comprising: an x-ray source configured to emit x-rays; an x-ray detector configured to generate spectral CT image data; a processor configured to determine a denoised linear estimate of the generated spectral CT image data based on maximizing or minimizing a first objective function; Including, The CT imaging system, wherein the processor is further configured to determine at least one parameter of the linear estimate by at least one machine learning system.

18. the processor is configured to process the spectral CT image data based on the at least one machine learning system to obtain a matrix W and a vector b, and form denoised spectral CT image data a according to a linear estimation according to a=WX+b; 18. The CT imaging system of claim 17, wherein x is a representation of spectral CT image data comprising at least two spectral components.

19. 20. The CT imaging system of claim 18, wherein at least one of the matrix W and the vector b is adjustable to enable optimization of at least one image quality index of the CT image data based on maximization or minimization of a second objective function.

20. 20. The CT imaging system of claim 18, wherein the at least one second objective function is at least one of mean squared error, structural similarity, bias, fine detail fidelity, numerical observer detectability, visual score, and observer performance.

21. The CT imaging apparatus according to claim 18 , wherein the matrix W is a diagonal matrix.

22. 20. The CT imaging system of claim 18, wherein the spectral CT image data includes at least one of a set of sinograms and a set of reconstructed images.

23. 20. The CT imaging system of claim 18, wherein at least one of the matrix W and the vector b of the denoised spectral CT image data a is adjustable by an end user.

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