Multi-valued mapping correction method suitable for CXCBI reconstruction based on coding aperture

Abstract

The invention belongs to the technical field of Compton back scattering imaging, and discloses a multi-valued mapping correction method suitable for a CXCBI reconstruction algorithm based on a coded aperture, and the specific technical scheme is as follows: determining parameters of an X-ray source, a detector and the coded aperture, determining an object to be measured and the position thereof, and collecting back scattering photon information of the object to be measured; the method comprises the following steps: constructing an observation value vector, inputting the observation value vector into a total variation regularization model, constructing a binary measurement matrix, correcting the binary measurement matrix into a multi-valued measurement matrix, inputting the multi-valued measurement matrix into the total variation regularization model on one hand to obtain an image initial value, and configuring an ADMM optimization strategy on the other hand, a three-dimensional block matching algorithm is adopted in the algorithm framework for denoising; when the image variance trend is smooth, ending iteration, and reconstructing an x vector to obtain a back scattering image result of the to-be-measured object; according to the invention, the position, shape and complex details of the to-be-detected object are reserved, and the detection capability of the system is improved excellently.

Description

Technical Field

[0001] The invention belongs to the technical field of Compton backscatter imaging, and in particular relates to a multi-value mapping correction method suitable for a CXCBI reconstruction algorithm based on a coded aperture. Background Art

[0002] At present, the application of X-ray Compton backscatter imaging (XCBI) technology in the field of security inspection has attracted much attention, especially for the one-sided detection of low-atomic-number and low-density contraband such as explosives and drugs. XCBI technology can be divided into three types: point scanning, line scanning and surface scanning according to the way the rays scan the object.

[0003] Point scanning XCBI technology uses a high-precision collimation mechanical structure composed of a fan-shaped collimator and a high-speed rotating chopper wheel to collimate the cone beam X-ray into a pencil beam with a small spot diameter, and uses it as a small-sized point source to scan the object in one dimension, and uses the relative motion between the imaging system and the object to complete the two-dimensional scanning of the object. Point-by-point scanning backscatter imaging uses a detector to capture the scattered photon information of each scattering point inside the object, and uses the energy and quantity information of the backscattered photons and their spatial position information to achieve two-dimensional image reconstruction. The point scanning XCBI system can improve the spatial resolution through a high-precision collimation structure. However, its high-precision collimation mechanical structure is large in size, the two-dimensional scanning of the object takes a long time, and the utilization rate of X-rays is very low. In addition, due to the time limit of the system focusing, real-time accurate focusing cannot be guaranteed during the movement of the object, which will lead to reduced imaging quality.

[0004] Line scanning XCBI technology is an optimization of the point-by-point scanning imaging structure. The high-speed rotating chopper wheel in the point-by-point scanning structure is replaced by pixel collimation of the linear array detector. After the cone beam X-ray passes through the fan collimator, it performs a one-dimensional line scan on the object in the form of a fan beam. The linear array detector detects all scattering points inside the object along the incident direction of the ray and uses the collimation structure matched with the pixels of the linear array detector to reduce the crosstalk between adjacent scattering points to improve the imaging resolution in the one-dimensional direction. It also requires the relative movement of the imaging system and the object to complete the two-dimensional scanning and detection of the object. Although the line scanning XCBI system reduces the system volume by simplifying the chopper wheel structure and improves the ray utilization rate to a certain extent, the pixel collimation structure of the linear array detector will lose some backscattered photons and introduce overlapping scattering areas in the backscattering reconstruction process, resulting in reduced image reconstruction quality.

[0005] The surface scanning XCBI technology uses cone beam rays to directly scan the entire scene of the object, and uses a planar array detector with a collimated structure to detect all scattering points on the corresponding plane in the object, collect scattered photon information, and reconstruct the image. Compared with point scanning and line scanning, the surface scanning XCBI technology has a more serious problem of crosstalk between adjacent scattering points, which makes the algorithm analysis complex and affects the quality of the reconstructed image. Therefore, the compressed X-ray Compton backscatter imaging (CXCBI) technology abandons the traditional high-precision collimation structure, combines it with the compressed sensing imaging theory, uses a two-dimensional coded aperture to perform structural encoding on the cone beam X-ray, performs backscatter imaging through sparse acquisition of object information and corresponding reconstruction algorithms, and converts the backscatter image reconstruction into an inverse problem optimization solution. The CXCBI technology greatly simplifies the system structure, and its difficulty lies in how to build a reconstruction algorithm model and correct the reconstruction deviation introduced by its physical structure.

[0006] For compressed X-ray Compton backscatter imaging (CXCBI) with full scene irradiation, the coded aperture (CA) is used to integrate the compressed sensing imaging theory with the backscatter imaging technology, which can solve the spatial positioning problem caused by the CXCBI full scene irradiation. However, since the cone beam X-ray itself has a certain transmission direction and the coding template has a certain thickness, the coded aperture unit boundary will introduce reconstruction deviation during the coded aperture projection process, resulting in a decrease in the quality of the backscatter reconstruction image. Therefore, it is of great significance to correct the coded aperture projection of the CXCBI system to improve the quality of the reconstructed image. Summary of the invention

[0007] In order to solve the technical problems existing in the prior art, the present invention provides a multi-value mapping correction method suitable for the CXCBI reconstruction algorithm based on coded aperture, which corrects the reconstruction deviation introduced by the coded aperture unit boundary to ensure the consistency of the reconstructed image results, thereby improving the accuracy of compressed X-ray Compton backscatter imaging technology in detecting targets.

[0008] To achieve the above object, the technical solution adopted by the present invention is: a multi-value mapping correction method suitable for CXCBI reconstruction based on coded aperture, the specific steps are as follows:

[0009] Step 1: determine the parameters of the X-ray source, detector, and coded aperture, determine the object to be measured and its position, and collect backscattered photon information of the object to be measured;

[0010] Step 2: Construct the observation vector y, input it into the total variation regularization model, construct the binary measurement matrix A, modify the binary measurement matrix to be the multi-value measurement matrix A1, input one aspect of the multi-value measurement matrix A1 into the total variation regularization model, and obtain the image initial value x 0 、z 0 、u 0 ,On the other hand, the multi-value measurement matrix A1 configures the ADMM optimization strategy, and adopts the three-dimensional block matching algorithm for ,denoising in the algorithm framework;

[0011] Step 3: When the image variance trend is flat, the iteration ends and the x vector is reconstructed to obtain the backscattered image result of the object to be measured.

[0012] In the X-ray Compton backscatter imaging system, the X-ray source emits in a cone beam, and the range of the ray irradiation needs to completely cover the object to be measured. A coded aperture structure is designed to perform structured encoding of the X-rays so that the X-rays irradiated on the object to be measured are randomly distributed and sparsely sampled.

[0013] The structure of the designed coded aperture is a rectangular parallelepiped with a thickness of t mm. If the resolution of the image to be reconstructed is n×n and the aperture spacing of the coded aperture is 2 mm, then the width of the coded aperture is at least 2n mm and the length is at least n(2+n)-2 mm. Such dimensions are selected in order to collect sufficient data. The coded aperture material is high-density metal tungsten, which has a large density and can block the penetration of X-rays with an energy lower than 120 kV at a thickness of 6 mm. The coded aperture is constructed by a random binary matrix, and the values ​​of the random binary matrix are only 0 and 1, and the proportion of 0 and 1 is 50% each. The coded aperture corresponding to the value 0 is a non-opening area, and the value 1 corresponds to an opening area.

[0014] After passing through the coded aperture area, the X-rays are irradiated onto the object to be measured, and the backscattered photon information is collected by a large-area single-pixel detector. Each time the coded aperture detector is moved, the backscattered photon information can be collected once. Finally, the image is restored by combining all the collected backscattered photon information with the reconstruction algorithm.

[0015] During image reconstruction, the size of the image to be reconstructed is n×n, and each column is concatenated together to reconstruct a length of n 2 The one-dimensional column vector x of the measurement matrix A is m×n 2 , y is a one-dimensional column vector containing m observations. The measurement matrix A can be a commonly used binary random matrix, and the value 1 or 0 corresponds to the open or non-open area on the coded aperture.

[0016] The area where the X-rays irradiate the coded aperture is a square area. Each column of the matrix corresponding to the aperture in the square area is also connected in series to obtain one row of the measurement matrix A. After the coded aperture moves horizontally by one column, the aperture in the square area changes, and new observations are collected on the detector. The number of columns moved by the coded aperture determines the number of rows of the measurement matrix A. If the size of the reconstructed image is 8×8, x has 64 pixel values, and the coded aperture moves a total of m-1 times (no movement is required during the initial acquisition), then there are m observations in y. The measurement matrix A has a total of m rows, and each row is reconstructed from the square matrix moving on the left.

[0017] In the image reconstruction algorithm, the measurement matrix error caused by the aperture edge of the coded aperture is corrected to obtain a multi-value measurement matrix that is more consistent with the effect of X-ray penetration of the coded aperture. The correction method is as follows:

[0018] The position coordinates of any aperture on the coded aperture are (x, y), its distance from the center of the coded aperture is L1, and the distance from the coded aperture to the center of the X-ray source is L2, then The thickness of the coded aperture is t, and α is the constraint factor coefficient of the coded aperture.

[0019] The influence factor μ of any aperture edge region on its corresponding measurement matrix value (x,y) It can be expressed as:

[0020]

[0021] After obtaining the influence factor of each aperture, the measurement matrix value of the corresponding position of the aperture is corrected. If there are q (q <= 4) non-opening apertures with opposite values ​​near a certain opening aperture, and the position coordinates of the opening aperture are (x1, y1), then the measurement matrix value 1 of the corresponding position of the opening aperture is corrected to On the contrary, if there are p (p <= 4) apertures with opposite values ​​near a non-aperture aperture, and the position coordinates of the non-aperture aperture are (x2, y2), then the measurement matrix value 0 at the corresponding position of the non-aperture aperture is corrected to The position coordinates (x1, y1) and (x2, y2) are both part of (x, y), and the corresponding measurement matrix numerical correction can be completed by traversing the aperture positions of all coded apertures.

[0022] For simplicity, when calculating the influence factor μ of the aperture, the coded aperture area through which the X-ray passes can be divided into a areas. The areas are distributed from the inside to the outside, and the influence factors of the apertures inside the areas are considered to be the same. After the influence factor of each area is calculated using formula (1), each aperture position can be traversed to correct the measurement matrix value of its corresponding position, and finally the corrected multi-value measurement matrix A1 is obtained.

[0023] The image reconstruction algorithm is based on the optimization strategy of the alternating direction multiplication method. The size of the image to be reconstructed is n×n. The coded aperture is moved m times, and the detector collects m backscattered photon information. This information constitutes the one-dimensional column vector y of the observed value. Each column of the image to be reconstructed is connected in series to form a one-dimensional column vector x. The measurement matrix corresponding to the coded aperture is A, and the corrected multi-value measurement matrix is ​​A1. The mathematical problem of reconstructing the entire image can be expressed as: y=A1x. The most direct way to solve this problem is to find the minimum l0 norm x corresponding to the observed value y. The corresponding mathematical model is:

[0024]

[0025] The alternating direction multiplier method is used to solve formula (2) to obtain the mathematical model (3):

[0026]

[0027] The augmented Lagrangian transformation of formula (3) yields formula (4):

[0028]

[0029] In formulas (2), (3), and (4), x is a one-dimensional vector containing N values. When the subscript value is r, st (such that) means that the following formula is a constraint of the previous formula (the same applies to other formulas), α is the optimization variable, σ T is the Lagrange multiplier, ρ is the penalty factor, and the values ​​of x, z, and u need to be updated alternately when solving. The alternating iterative update formula is:

[0030] x k+1 =(A1 T A1+ρI) -1 (A1 T y+ρ(z k -u k )) (5)

[0031]

[0032] u k+1 =u k +x k+1 -z k+1 (7)

[0033] In formulas (5), (6), and (7), x is the one-dimensional column vector of the image to be reconstructed, y is the one-dimensional column vector of the observations collected on the detector, A1 is the corrected measurement matrix, ρ is the penalty factor, I is the identity matrix, z and u are the intermediate variables of the problem reconstructed using augmented Lagrange multipliers, λ is the optimization variable, and σ 2is the noise variance, is a denoiser, using a 3D block matching denoising algorithm. The initial image x 0 Usually, it is a matrix with all values ​​0. In order to make the iteration faster, the total variation (TV) regularization model is used to obtain an initial image containing more information. The mathematical model is:

[0034]

[0035] Among them, D i x is the discrete gradient value of each pixel i in x, and the slack variable w is introduced into the model (8) so that D i x=w, the model can be changed to:

[0036]

[0037] Among them, v, λ are Lagrange multipliers, β i , μ is the penalty factor, and the optimal solution of the augmented Lagrangian problem is solved by an iterative method. The iterative update formula of the Lagrangian multiplier is:

[0038] v i k+1 =v i k -β i k (D i x k+1 -w i k+1 ) (10)

[0039] λ k+1 =λ k+1 -μ i k (A1x k+1 -y) (11)

[0040] Where k is the number of iterations, solving for w i k+1 When you first put x k Treat it as a constant and solve for w i k+1 The formula is:

[0041]

[0042] Setting the subdifferential of formula (12) equal to zero, we can find w i k+1 The optimal solution of w i k+1 We can get x k+1 The formula is:

[0043]

[0044] After finding the gradient of formula (13), the single-step descent method can be used to find x k+1 The optimal solution of k+1 Save as the initial value, and before iterating formulas (5), (6), and (7), set x 0 、z 0 、u 0 The value of is equal to the value of x obtained by formula (13) k +1 The optimal solution, the condition for the termination of the iteration is set to that the image variance of the next iteration changes less than a fixed value of 10 compared with the previous iteration. After the iteration is terminated, the backscattered image result capable of detecting the object to be tested is obtained.

[0045] Compared with the prior art, the present invention has the following specific beneficial effects: the present invention proposes a backscatter image reconstruction deviation correction method based on multi-value mapping. The correction method of the present invention effectively reduces the penetration error of X-rays at the edge of the binary matrix corresponding to the coded aperture, and the re-measurement matrix construction is more in line with the actual situation of X-ray penetration of the coded aperture. The measurement matrix is ​​corrected from the previous binary measurement matrix to a multi-value measurement matrix and re-added to the image reconstruction algorithm. When reconstructing an image of a low-density material containing complex details, the backscatter image reconstructed by the correction method can more clearly observe the position and shape of the object to be measured, retain the complex details, and greatly improve the detection capability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flow chart of the backscatter image reconstruction deviation correction method based on multi-value mapping.

[0047] Figure 2 This is the structure diagram of the compressed X-ray Compton backscatter imaging (CXCBI) system.

[0048] Figure 3 It is a relationship diagram between the measurement matrix, image vector and observation vector.

[0049] Figure 4 Schematic diagram of the coded aperture structure.

[0050] Figure 5 Schematic diagram of part of the area for correcting the measurement matrix.

[0051] Figure 6 Backscattered image of the palm model CXCBI system obtained by the uncorrected measurement matrix.

[0052] Figure 7 This is the backscattered image of the palm model CXCBI system obtained after correcting the measurement matrix. DETAILED DESCRIPTION

[0053] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0054] like Figure 1 As shown, a multi-value mapping correction method suitable for CXCBI reconstruction based on coded aperture, the specific steps are as follows:

[0055] Step 1: Determine the parameters of the X-ray source, detector, and coded aperture, determine the object to be measured and its position, and collect backscattered photon information of the object to be measured.

[0056] Step 2. During the specific implementation of this method, the CXCBI system sets the X-ray energy to 120 KeV, the detector is made of sodium iodide material, and a palm (density 1 g / cm3) model is detected. The middle finger of the palm has a gold ring (Z=79, density 19.3 g / cm3).

[0057] First, the CXCBI system is used to collect backscattered photon information. The coded aperture used is 2 mm aperture spacing, and the X-ray penetration area is 32×32 aperture area. At this time, the transmittance in the area is 50%. The coded aperture moves one column each time, and moves 511 times in total to collect 512 backscattered photon information data. After obtaining the backscattered photon information, it is constructed into an observation value matrix y and input into the total variation regularization model to construct a binary measurement matrix A. The binary measurement matrix is ​​corrected to be a multi-value measurement matrix A1. One side of the multi-value measurement matrix A1 is input into the total variation regularization model to obtain the image initial value x 0 、z 0 、u 0 ,On the other hand, the multi-value measurement matrix A1 configures the ADMM optimization strategy, and adopts the three-dimensional block matching algorithm for ,denoising in the algorithm framework.

[0058] Step 3: When the image variance trend is flat, the iteration ends and the x vector is reconstructed to obtain the backscattered image result of the object to be measured.

[0059] In the X-ray Compton backscatter imaging system, the X-ray source emits in a cone beam, and the range of the ray irradiation needs to completely cover the object to be measured. A coded aperture structure is designed to perform structured encoding of the X-rays so that the X-rays irradiated on the object to be measured are randomly distributed and sparsely sampled.

[0060] The structure of the designed coded aperture is a rectangular parallelepiped with a thickness of t mm. If the resolution of the image to be reconstructed is n×n and the aperture spacing of the coded aperture is 2 mm, then the width of the coded aperture is at least 2n mm and the length is at least n(2+n)-2 mm. Such dimensions are selected in order to collect sufficient data. The coded aperture material is high-density metal tungsten, which has a large density and can block the penetration of X-rays with an energy lower than 120 kV at a thickness of 6 mm. The coded aperture is constructed by a random binary matrix, and the values ​​of the random binary matrix are only 0 and 1, and the proportion of 0 and 1 is 50% each. The coded aperture corresponding to the value 0 is a non-opening area, and the value 1 corresponds to an opening area.

[0061] After X-rays pass through the coded aperture area, they are irradiated onto the object to be measured. The large-area single-pixel detector collects backscattered photon information. Each time the coded aperture detector is moved, backscattered photon information can be collected once. Finally, the image is restored by combining all the collected backscattered photon information with the reconstruction algorithm. The schematic diagram of the structure of the X-ray Compton backscatter imaging system based on the coded aperture is shown in the figure. Figure 2 shown.

[0062] During image reconstruction, the size of the image to be reconstructed is n×n, and each column is concatenated together to reconstruct a length of n 2 The one-dimensional column vector x of the measurement matrix A is m×n 2 , y is a one-dimensional column vector containing m observations. The measurement matrix A can be a commonly used binary random matrix, and the value 1 or 0 corresponds to the open or non-open area on the coded aperture.

[0063] The area where the X-rays irradiate the coded aperture is a square area. Each column of the matrix corresponding to the aperture in the square area is also connected in series to obtain one row of the measurement matrix A. When the coded aperture moves horizontally by one column, the aperture in the square area changes, and new observation values ​​are collected on the detector. The number of columns that the coded aperture moves determines the number of rows of the measurement matrix A.

[0064] exist Figure 3 In the example, if the size of the reconstructed image is 8×8, x has 64 pixel values, and the coded aperture moves a total of m-1 times (no movement is required during the initial acquisition), then there are m observations in y, and the measurement matrix A has a total of m rows, each of which is reconstructed from the square matrix moving on the left.

[0065] In the image reconstruction algorithm, the measurement matrix error caused by the aperture edge of the coded aperture is corrected to obtain a multi-value measurement matrix that is more consistent with the effect of X-ray penetration of the coded aperture. The correction method is as follows:

[0066] The position coordinates of any aperture on the coded aperture are (x, y), its distance from the center of the coded aperture is L1, and the distance from the coded aperture to the center of the X-ray source is L2, then The thickness of the coded aperture is t, α is the constraint factor coefficient of the coded aperture, and the schematic diagram of the coded aperture structure is shown in Figure 4 shown.

[0067] The influence factor μ of any aperture edge region on its corresponding measurement matrix value (x,y) It can be expressed as:

[0068]

[0069] After obtaining the influence factor of each aperture, the measurement matrix value of the corresponding position of the aperture is corrected. If there are q (q <= 4) non-opening apertures with opposite values ​​near a certain opening aperture, and the position coordinates of the opening aperture are (x1, y1), then the measurement matrix value 1 of the corresponding position of the opening aperture is corrected to On the contrary, if there are p (p <= 4) apertures with opposite values ​​near a non-aperture aperture, and the position coordinates of the non-aperture aperture are (x2, y2), then the measurement matrix value 0 at the corresponding position of the non-aperture aperture is corrected to The position coordinates (x1, y1) and (x2, y2) are both part of (x, y), and the corresponding measurement matrix numerical correction can be completed by traversing the aperture positions of all coded apertures.

[0070] For simplicity, when calculating the influence factor μ of the aperture, the coded aperture area through which the X-ray passes is divided into a areas, and the areas are distributed from the inside to the outside. The influence factors of the apertures within the areas are considered to be the same. After the influence factor of each area is calculated using formula (1), each aperture position can be traversed to correct the measurement matrix value of its corresponding position, and finally the corrected multi-value measurement matrix A1 is obtained. The binary measurement matrix is ​​transformed into a multi-value measurement matrix. The schematic diagram of some areas is as follows: Figure 5 shown.

[0071] The image reconstruction algorithm is based on the optimization strategy of the alternating direction multiplication method. The size of the image to be reconstructed is n×n. The coded aperture is moved m times, and the detector collects m backscattered photon information. This information constitutes the one-dimensional column vector y of the observed value. Each column of the image to be reconstructed is connected in series to form a one-dimensional column vector x. The measurement matrix corresponding to the coded aperture is A, and the corrected multi-value measurement matrix is ​​A1. The mathematical problem of reconstructing the entire image can be expressed as: y=A1x. The most direct way to solve this problem is to find the minimum l0 norm x corresponding to the observed value y. The corresponding mathematical model is:

[0072]

[0073] The alternating direction multiplier method is used to solve formula (2) to obtain the mathematical model (3):

[0074]

[0075] The augmented Lagrangian transformation of formula (3) yields formula (4):

[0076]

[0077] In formulas (2), (3), and (4), x is a one-dimensional vector containing N values. When the subscript value is r, st (such that) means that the following formula is a constraint of the previous formula (the same applies to other formulas), α is the optimization variable, σ T is the Lagrange multiplier, ρ is the penalty factor, and the values ​​of x, z, and u need to be updated alternately when solving. The alternating iterative update formula is:

[0078] x k+1 =(A1 T A1+ρI) -1 (A1 T y+ρ(z k -u k )) (5)

[0079]

[0080] u k+1 =u k +x k+1 -z k+1 (7)

[0081] In formulas (5), (6), and (7), x is the one-dimensional column vector of the image to be reconstructed, y is the one-dimensional column vector of the observations collected on the detector, A1 is the corrected measurement matrix, ρ is the penalty factor, I is the identity matrix, z and u are the intermediate variables of the problem reconstructed using augmented Lagrange multipliers, λ is the optimization variable, and σ 2 is the noise variance, is a denoiser, using a 3D block matching denoising algorithm. The initial image x 0 Usually, it is a matrix with all values ​​0. In order to make the iteration faster, the total variation (TV) regularization model is used to obtain an initial image containing more information. The mathematical model is:

[0082]

[0083] Among them, D i x is the discrete gradient value of each pixel i in x, and the slack variable w is introduced into the model (8) so that D i x=w, the model can be changed to:

[0084]

[0085] Among them, v, λ are Lagrange multipliers, β i , μ is the penalty factor, and the optimal solution of the augmented Lagrangian problem is solved by an iterative method. The iterative update formula of the Lagrangian multiplier is:

[0086] v i k+1 =v i k -β i k (D i x k+1 -w i k+1 ) (10)

[0087] λ k+1 =λ k+1 -μ i k (A1x k+1 -y) (11)

[0088] Where k is the number of iterations, solving for w i k+1 When you first put x k Treat it as a constant and solve for w i k+1 The formula is:

[0089]

[0090] Setting the subdifferential of formula (12) equal to zero, we can find w i k+1 The optimal solution of w i k+1 We can get x k+1 The formula is:

[0091]

[0092] After finding the gradient of formula (13), the single-step descent method can be used to find x k+1 The optimal solution of k+1 Save as the initial value, and before iterating formulas (5), (6), and (7), set x 0 、z 0 、u 0 The value of is equal to the value of x obtained by formula (13) k +1 The optimal solution, the condition for the termination of the iteration is set to that the image variance of the next iteration changes less than a fixed value of 10 compared with the previous iteration. After the iteration is terminated, the backscattered image result capable of detecting the object to be tested is obtained.

[0093] Finally, the ADMM optimization strategy algorithm framework is used to reconstruct the backscattered image, and the flying spot scanning system is used to obtain a clear backscattered image Ground-Truth for index analysis.

[0094] The backscattered image of the palm model CXCBI system obtained by the uncorrected measurement matrix is ​​as follows Figure 6 As shown in the figure, it can be found that the palm model reconstructed with 128 data points cannot distinguish the shape at all. Although the backscattered image reconstructed with 256 data points can be observed as the shape of the palm, it lacks the shape of the little finger. The backscattered image reconstructed with 512 data points has a better effect, but the area of ​​the gold ring on the middle finger is not obvious enough, and it is not certain whether the gold ring exists. The corresponding index results with the Ground-Truth clear image are shown in Table 1.

[0095] Table 1: Figure 6 Comparison results of the backscattered image reconstructed in the image and the Ground-Truth image

[0096]

[0097] The backscattered image of the palm model CXCBI system obtained after correcting the measurement matrix is ​​as follows: Figure 7 As shown, it can be found that the palm model reconstructed with 128 data points can already distinguish the shape of the palm, the backscatter image reconstructed with 256 data points can already observe the complete shape of the palm, and the area of ​​the gold ring on the middle finger of the backscatter image reconstructed with 512 data points is obvious, and the existence of the gold ring can be confirmed. The corresponding indicator results with the Ground-Truth clear image are shown in Table 2.

[0098] Table 2: Figure 7 Comparison results of the backscattered image reconstructed in the image and the Ground-Truth image

[0099]

[0100] By comparing Table 1 and Table 2, it can be found that the backscatter image indicators reconstructed by the correction method under different data amounts are improved to a certain extent, and the improvement effect is more obvious under lower data amounts, which preliminarily confirms the feasibility and effectiveness of the method.

[0101] The present invention proposes a backscatter image reconstruction deviation correction method based on multi-value mapping for the CXCBI system. The method effectively reduces the penetration error of X-rays at the edge of the binary matrix corresponding to the coded aperture. The reconstructed backscatter image can more clearly observe the position and shape of the object to be measured, retains complex details, and greatly improves the detection capability of the system.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. A multi-value mapping correction method suitable for coded aperture-based CXCBI reconstruction, characterized in that: The specific steps are as follows: Step 1: determine the parameters of the X-ray source, detector, and coded aperture, determine the object to be measured and its position, and collect backscattered photon information of the object to be measured; Step 2: Construct the observation vector y, input it into the total variation regularization model, construct the binary measurement matrix A, modify the binary measurement matrix to be the multi-value measurement matrix A1, input one aspect of the multi-value measurement matrix A1 into the total variation regularization model, and obtain the image initial value x 0 、z 0 、u 0 ,On the other hand, the multi-value measurement matrix A1 configures the ADMM optimization strategy, and adopts the three-dimensional block matching algorithm for ,denoising in the algorithm framework; Step 3: When the image variance trend is flat, the iteration ends and the x vector is reconstructed to obtain the backscattered image result of the object to be measured.

2. The multi-value mapping correction method for coded aperture-based CXCBI reconstruction according to claim 1, characterized in that: In step 2, the position coordinates of any aperture on the coded aperture are set to (x, y), the distance between the position coordinates and the center of the coded aperture is L1, and the distance between the coded aperture and the center of the X-ray source is L2, then The thickness of the coded aperture is t, and α is the constraint factor coefficient of the coded aperture; The influence factor μ of any aperture edge area on its corresponding measurement matrix value (x,y) It is expressed as: After obtaining the influence factor of each aperture, the measurement matrix value of the corresponding position of the aperture is corrected. If there are q (q <= 4) non-opening apertures with opposite values ​​near a certain opening aperture, and the position coordinates of the opening aperture are (x1, y1), then the measurement matrix value 1 of the corresponding position of the opening aperture is corrected to If there are p (p<=4) opening apertures with opposite values ​​near a non-opening aperture, and the position coordinates of the non-opening aperture are (x2, y2), then the measurement matrix value 1 at the corresponding position of the non-opening aperture is corrected to 0+p Correction of the corresponding measurement matrix values ​​is completed by traversing the aperture positions of all coded apertures; When calculating the influence factor μ of the aperture, the coded aperture area through which the X-ray passes is divided into a areas, and the areas are distributed from the inside to the outside. The influence factors of the apertures within the areas are considered to be the same. After the influence factor of each area is calculated using formula (1), each aperture position is traversed to correct the measurement matrix value of its corresponding position, and finally the corrected multi-value measurement matrix A1 is obtained; The image reconstruction algorithm is based on the optimization strategy of the alternating direction multiplier method. The size of the image to be reconstructed is n×n. The coded aperture is moved m times, and the detector collects m backscattered photon information. This information constitutes the one-dimensional column vector y of the observed value. Each column of the image to be reconstructed is connected in series to form a one-dimensional column vector x. The measurement matrix corresponding to the coded aperture is A, and the corrected multi-value measurement matrix is ​​A1. The mathematical problem of reconstructing the entire image is expressed as: y=A1x. The most direct way to solve this problem is to find the minimum l0 norm x corresponding to the observed value y. The corresponding mathematical model is: The alternating direction multiplier method is used to solve formula (2) to obtain the mathematical model (3): The augmented Lagrangian transformation of formula (3) yields formula (4): In formulas (2), (3), and (4), st represents that the latter formula is a constraint condition of the former formula, α is the optimization variable, and σ T is the Lagrange multiplier, ρ is the penalty factor, and the values ​​of x, z, and u are updated alternately during the solution. The alternating iterative update formula is: x k+1 =(A1 T A1+ρI) -1 (A1 T y+ρ(z k -u k )) (5) u k+1 =u k +x k+1 -z k+1 (7) In formulas (5), (6), and (7), x is the one-dimensional column vector of the image to be reconstructed, y is the one-dimensional column vector of the observations collected on the detector, A1 is the corrected measurement matrix, ρ is the penalty factor, I is the identity matrix, z and u are the intermediate variables for reconstructing the problem using augmented Lagrange multipliers, λ is the optimization variable, σ 2 is the noise variance, As a denoiser, a three-dimensional block matching denoising algorithm is used, and the total variation regularization model is used to obtain the initial value x 0 , the mathematical model is: Among them, D i x is the discrete gradient value of each pixel i in x, and the slack variable w is introduced into the model (8) so that D i x=w, the model changes to: Among them, v and λ are Lagrange multipliers, β i , μ is the penalty factor, and the optimal solution of the augmented Lagrangian problem is solved by an iterative method. The iterative update formula of the Lagrangian multiplier is: v i k+1 =v i k -β i k (D i x k+1 -w i k+1 ) (10) l k+1 =λ k+1 -m i k (A1x k+1 -y) (11) Where k is the number of iterations, solving for w i k+1 When you first put x k Treat it as a constant and solve for w i k+1 The formula is: Let the sub-differential of formula (12) be zero and find w i k+1 The optimal solution of w i k+1 Get x k+1 The formula is: After finding the gradient of formula (13), the single-step descent method is used to find x k+1 The optimal solution of k+1 Save as the initial value, and before iterating formulas (5), (6), and (7), set x 0 、z 0 、u 0 The value of is equal to the value of x obtained by formula (13) k+1 The optimal solution, the condition for the termination of the iteration is set to that the image variance of the next iteration changes less than a fixed value of 10 compared with the previous iteration. After the iteration is terminated, the backscattered image result of the object to be tested is obtained.

Images