Energy spectrum CT image reconstruction method and device based on joint regularization

Abstract

The present invention relates to the field of energy spectrum computer tomography technology, and discloses an energy spectrum CT image reconstruction method and device based on joint regularization. The method solves the image reconstruction problem under noise interference and incomplete data conditions by introducing two joint regularization energy functions and designing an efficient solution algorithm based on the alternating direction multiplier method. The method first constructs a high-dimensional tensor with similar blocks between multi-channel images, then introduces a weighted tensor nuclear norm to characterize the low rank property of the tensor, and finally designs an efficient solution algorithm based on the alternating direction multiplier method. Compared with existing methods, this method can effectively integrate the calculation process of minimizing the weighted tensor nuclear norm and the image gradient domain L0 norm, and the feasibility of the method has been verified in experiments on low-dose problems and incomplete data problems.

Description

Technical Field

[0001] The present invention relates to the technical field of spectral computed tomography, and in particular to a spectral CT image reconstruction method and device based on joint regularization. Background Art

[0002] Multi-energy computed tomography (MECT) technology offers energy-resolved imaging capabilities for material attenuation distribution, effectively suppressing hardening artifacts and enabling quantitative analysis of material composition, promising broad applications in medicine. Currently, MECT imaging systems primarily utilize four scanning schemes: multi-scan systems, rapid kVp switching systems, multi-source multi-detector systems, and photon-counting detector systems. However, these scanning schemes may face challenges such as excessive radiation exposure, incomplete data, or interference from strong photon statistical noise. Therefore, designing efficient and feasible reconstruction algorithms to effectively address these challenges has become a research hotspot in the MECT imaging field.

[0003] To address the problems of incomplete data and low-dose, high-noise imaging, numerous research groups have conducted extensive research. Driven by compressed sensing theory, regularization methods based on sparse priors have been widely used in CT image reconstruction. Among them, the total variation (TV) minimization model has become a popular approach for dealing with incomplete data. In 2008, Pan Xiaochuan's team proposed the Adaptive Steepest Descent Projection Onto Convex Sets (ASD-POCS) algorithm, applying the TV minimization model to CT image reconstruction. This algorithm uses convex set projection to enforce image constraints and adaptive steepest descent to minimize the total variation of the image. In 2012, Wang Ge's team applied TV regularization to MECT imaging. Using TV regularization to constrain CT images of different energies, they suppressed artifacts caused by incomplete data to a certain extent and achieved better reconstruction results. However, MECT multi-channel images have strong correlations, and the TV minimization model method cannot well describe this prior characteristic.

[0004] In recent years, tensor methods have provided new ideas for processing the low-rank characteristics in MECT high-dimensional structural data. In 2016, Ma Jianhua's team constrained the high-order derivatives of MECT images by introducing structural tensor TV regularization, and proposed a penalized weighted least squares reconstruction method based on structural tensor TV regularization. In 2018, Wu Weiwen and others used tensor dictionary learning to characterize the similarity between images of different energies, and proposed an L0 tensor dictionary learning MECT reconstruction method, but the dictionary learning method is highly dependent on training data, and the parameters of the model are relatively large. Subsequently, in 2019, Zhang Yi's team extracted similar blocks from multi-channel images and formed them into tensor form, and then decomposed them into low-rank components and sparse components to suppress noise and artifacts, and proposed a tensor MECT reconstruction algorithm for self-similarity of energy spectrum images. In the same year, Chen Yang's team proposed a tensor-enhanced sparse reconstruction method for spectral image similarity based on the low-rank decomposition of the Candecomp / Parafac (CP) tensor (SISTER). This method combines image gradient L0 norm minimization, tensor decomposition, and non-local similarity for sparse angular MECT reconstruction. The feasibility of the proposed method was verified experimentally. However, the CP decomposition requires multiple iterations of the alternating least squares method to converge, resulting in high computational complexity and room for improvement in computational efficiency. Summary of the Invention

[0005] In response to the problems of existing spectral CT reconstruction methods, such as the inability to well describe the prior characteristics and the need to improve computational efficiency, the present invention proposes a spectral CT image reconstruction method and device based on joint regularization. The present invention can effectively characterize the prior characteristics of spectral CT images, thereby reducing radiation dose and improving imaging efficiency.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] In one aspect, the present invention proposes a spectral CT image reconstruction method based on joint regularization, comprising:

[0008] Step 1: Use similar block matching to preprocess the collected multi-channel projection data to obtain a high-dimensional similar block tensor constructed with similar blocks;

[0009] Step 2: For the extracted high-dimensional similarity block tensor, the joint regularization framework is used to extract the low rank of the multi-channel image and the sparsity of the single-channel image respectively, and then the reconstructed energy spectrum CT image is obtained.

[0010] Furthermore, the step 1 includes: selecting a noise image under a channel to perform similar image block matching, and extracting corresponding similar blocks at the same position under different channels to form a tensor form.

[0011] Furthermore, the step 2 includes:

[0012] Construct the reconstruction model as follows:

[0013]

[0014] in, represents the estimated reconstructed energy spectrum CT image; p s =Ax s +ε s ,s=1,2,...,S,, S is the total energy level of X-rays, s is its index, represents the projection data collected at the s energy level, h represents the projection data collected at a single energy level; A∈R h×g represents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Indicates the error between the true value and the estimated value; is the data fidelity term; R1(x) represents the weighted tensor nuclear norm regularization, which is used to achieve low-rank characterization of multi-channel images. represents the t-th similar block tensor, t=1,...,T, T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor; R2(x) represents the L0 norm regularization of the image gradient domain, which is used to realize the sparsity characterization of single-channel images. ω and ρ are the weights for balancing the two regularization terms and the fidelity term;

[0015] The constrained reconstruction model is converted into an unconstrained form using the augmented Lagrangian function, and the model is solved using the alternating direction multiplier method.

[0016] Another aspect of the present invention provides a spectral CT image reconstruction device based on joint regularization, comprising:

[0017] A similar block tensor construction module is used to pre-process the collected multi-channel projection data using a similar block matching operation to obtain a high-dimensional similar block tensor constructed with similar blocks;

[0018] The image reconstruction module is used to extract the low rank of multi-channel images and the sparsity of single-channel images from the extracted high-dimensional similar block tensors using a joint regularization framework, thereby obtaining the reconstructed energy spectrum CT image.

[0019] Furthermore, the similar block tensor construction module is specifically used to: select a noise image under a channel to perform similar image block matching, and extract corresponding similar blocks at the same position under different channels to form a tensor form.

[0020] Furthermore, the image reconstruction module is specifically used to:

[0021] Construct the reconstruction model as follows:

[0022]

[0023] in, represents the estimated reconstructed energy spectrum CT image; p s =Ax s +ε s ,s=1,2,...,S,, S is the total energy level of X-rays, s is its index, represents the projection data collected at the s energy level, h represents the projection data collected at a single energy level; A∈R h×g represents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Indicates the error between the true value and the estimated value; is the data fidelity term; R1(x) represents the weighted tensor nuclear norm regularization, which is used to achieve low-rank characterization of multi-channel images. represents the t-th similar block tensor, t=1,...,T, T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor; R2(x) represents the L0 norm regularization of the image gradient domain, which is used to realize the sparsity characterization of single-channel images. ω and ρ are the weights for balancing the two regularization terms and the fidelity term;

[0024] The constrained reconstruction model is converted into an unconstrained form using the augmented Lagrangian function, and the model is solved using the alternating direction multiplier method.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] By introducing image gradient domain L0 norm regularization and weighted tensor nuclear norm regularization, the present invention can effectively characterize the prior characteristics of energy spectrum CT images, thereby reducing radiation dose and improving imaging efficiency. The feasibility of the present invention has been verified in experiments studying low-dose problems and incompleteness problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flowchart of a method for spectral CT image reconstruction based on joint regularization according to an embodiment of the present invention;

[0028] Figure 2 Constructing a similar block tensor diagram for similar block matching;

[0029] Figure 3 The reconstruction results of different algorithms under the incomplete data problem; (a) is the reconstruction result of [16-22)keV; (b) is the reconstruction result of [28-31)keV; (c) is the reconstruction result of [41-50)keV; 1, 2, 3, 4 correspond to the SART algorithm, ASD-POCS algorithm, SISTER algorithm, and the method in this paper, respectively;

[0030] Figure 4 The profile diagrams of the reconstruction results of different algorithms under the incomplete data problem; (a) is the [16-22)keV profile result; (b) is the [28-31)keV profile result; (c) is the [41-50)keV profile result;

[0031] Figure 5 This is a list of quantitative evaluation results of PSNR of images reconstructed from simulated data using different algorithms under incomplete data problems.

[0032] Figure 6 The reconstruction results of different algorithms under low-dose problems; (a) is the reconstruction result of [16-22)keV; (b) is the reconstruction result of [28-31)keV; (c) is the reconstruction result of [41-50)keV; 1, 2, 3, 4 correspond to the SART algorithm, ASD-POCS algorithm, SISTER algorithm, and the method in this paper, respectively;

[0033] Figure 7 The following are the profiles of the reconstruction results of different algorithms under low-dose problems; (a) is the [16-22)keV profile result; (b) is the [28-31)keV profile result; (c) is the [41-50)keV profile result;

[0034] Figure 8 The following is a list of quantitative evaluation results of PSNR of images reconstructed by different algorithms for low-dose problems;

[0035] Figure 9 This is the convergence curve of the RMSE logarithm under low-dose problems. DETAILED DESCRIPTION

[0036] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0037] like Figure 1 As shown, a spectral CT image reconstruction method based on joint regularization includes:

[0038] Step 1: Construct a high-dimensional tensor using similar blocks between multi-channel images, such as Figure 2 As shown:

[0039] Tensor is a data representation in high-dimensional space. The basic form can be represented by a multidimensional array Represents a tensor. With the matrix The modulo n tensor product of is defined as the tensor Recorded as Tensor Each element can be defined as The higher order singular value decomposition (HOSVD) of a tensor is defined based on the modulo n tensor product, which is expressed as:

[0040]

[0041] In the above formula, Represents the core tensor of HOSVD, U i is the decomposition matrix in the modulo n direction, and satisfies

[0042] In order to extract the low-rank and sparse characteristics between images at different energies, this paper uses similar block matching to preprocess the energy spectrum image. In the experiment, a noise image f under a channel is selected, and similar image block matching is performed on f. Then, the corresponding similar blocks are extracted at the same position under different channels, and finally a tensor form is formed, which is called similar block tensor. The similar block matching operation can be described as Where t = 1, ..., T, T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor.

[0043] Step 2: Introduce the weighted tensor nuclear norm to characterize the intrinsic low rank of the image:

[0044] The present invention is based on the third-order tensor characterization of energy spectrum image data. For a given third-order tensor By further utilizing the weighted tensor nuclear norm to approximately characterize the rank of the tensor, it is expressed as:

[0045]

[0046] in, Representing a tensor Different principal components U under each mode i The intensity of b k Indicates each The corresponding non-negative weight. Non-negative weight b k For different The singular value penalty is different. The study found that the parameter setting of small penalty for large singular values ​​and large penalty for small singular values ​​is conducive to high-quality restoration of noisy images. In the present invention, the non-negative weight of the l+1th iteration is Set to The inverse proportion is expressed as:

[0047]

[0048] Among them, c is set to 4e-2; Set to 1e-5 to avoid division by zero.

[0049] Based on the preprocessing of similar block matching operations, the weighted nuclear norm minimization model can be further described as:

[0050]

[0051] Among them, T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor. On this basis, HOSVD is introduced. The weighted nuclear norm minimization model can be effectively solved. The solution steps of this method are as follows:

[0052] (a) Input: σ 2 .

[0053] (b) Using HOSVD Decompose it and get U1, U2, U3.

[0054] (c) Utilization Update the core tensor

[0055] (d) Get the updated

[0056] Step 3: Combine the image gradient domain L0 norm to characterize the image sparsity within the channel:

[0057] Sparse representation theory, also known as compressed sensing, has recently been widely applied to various aspects of signal processing due to its significant theoretical breakthroughs, particularly its reduced computational complexity. As a special type of signal, images themselves and the semantics they reflect often exhibit sparseness, which has led to the introduction of sparse representation theory into image processing. Image sparsity refers to the fact that, after a certain transformation, the image signal becomes mostly zero in the transformed domain. The image is said to be sparse or compressible. The image transformation process is the process of sparse representation. An image is sparsely decomposed on a set of overcomplete dictionaries (basis). The original image signal is represented by the fewest possible atoms in this dictionary, resulting in a sparse vector. This sparse vector is called the sparse representation of the image signal on this basis. This sparse representation allows the original image to be reconstructed with a high probability, significantly reducing storage and computational requirements. This gives the theory significant advantages in super-resolution reconstruction, image inpainting, and image analogy.

[0058] Based on the sparsity or compressibility of the original signal, the sampling and compression processes are performed synchronously, and the original signal can be accurately restored at a sampling rate far lower than the Nyquist sampling rate. The high-performance sparse reconstruction algorithm is an important guarantee for the successful application of sparse representation theory to actual sampling systems and data models. The sparse optimization problem based on the L0 norm constraint is the essential problem of sparse reconstruction. Since minimizing the L0 norm is NP-hard, recovery methods such as greedy algorithms, convex relaxation algorithms (using L1 norm instead of L0), and Bayesian compressed sensing have been developed. In addition to the above method, the present invention also considers the use of proxy functions to achieve approximation to the L0 norm, typical representatives of which are SL0 and ISL0 algorithms. The proxy function here refers to a certain type of parameterized smooth and differentiable continuous function. By adjusting its parameters, a smooth approximation of the L0 norm can be obtained, thereby better characterizing the sparsity of the image in the channel.

[0059] Step 4: Design an alternating direction multiplier method solution algorithm based on the joint regularization framework:

[0060] Since the acquisition of multi-energy projection data is susceptible to interference from noise and hardware environment factors, in order to better approximate the actual projection data acquisition process, the formula of the discrete linear system of CT imaging at the s energy level is expressed as:

[0061] p s =Ax s +ε s ,s=1,2,...,S, (5)

[0062] in, Represents the collected projection data, h represents the projection data collected under a single energy; A∈R h×grepresents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Represents the error between the true value and the estimated value. Based on this, for the extracted similar block tensor, the present invention uses a joint regularization framework to extract the intrinsic low rank of the multi-channel image and the sparsity of the image within the channel. The proposed reconstruction model is expressed as:

[0063]

[0064] in, is the data fidelity term. In order to facilitate the description of the formula, the present invention uses replace

[0065] In model (6), the present invention introduces two regularization models R1(x) and R2(x), where R1(x) represents weighted tensor nuclear norm regularization, specifically realizing the low-rank characterization of multi-channel images, which is expressed as T is the total number of similar block tensors, and t is its index; R2(x) represents the L0 norm regularization of the image gradient domain, which specifically realizes the sparsity characterization of single-channel images and is expressed as S is the total number of X-ray energy levels, s is its index; ω and ρ are the weights that balance the two regularization terms and the fidelity term. Introducing two regularization models, model (6) is further expressed as:

[0066]

[0067] In order to effectively solve the model (7), the present invention introduces two auxiliary variables, namely and y s =x s Therefore, model (7) is equivalent to the following model:

[0068]

[0069] By using the augmented Lagrangian function, the constrained reconstruction model (8) is transformed into an unconstrained form, which is expressed as:

[0070]

[0071] In the above formula, and e s Denotes the Lagrange multiplier, β and θ denote the penalty term coefficients. The present invention uses the alternating direction multiplier method to solve the model (9), which is decomposed into three sub-problems, namely x s , and y s Sub-questions:

[0072] (a) x in the lth iteration s The subproblem can be written as:

[0073]

[0074] Will and The elements in are rearranged into vector form along the directions of modulo 1, modulo 2 and modulo 3, and the vector is represented as z t ,P t (x) and v t , based on this, x s The sub-problem can also be expressed as:

[0075]

[0076] It can be found that the above formula is a quadratic function minimization problem. The quadratic agent algorithm is used to solve it and the updated x is obtained. s The formula is:

[0077]

[0078] in, In update x s Previously, the present invention first applied the Simultaneous Algebraic Reconstruction Technique (SART) algorithm to reconstruct CT images at different energies.

[0079] (b) In the first iteration The subproblem can be written as:

[0080]

[0081] The form of this sub-problem is the same as that of model (5), and can be iteratively updated through the solution steps described in Table 1.

[0082] (c) y in the lth iteration s The subproblem can be written as:

[0083]

[0084] This is a typical L0 minimization problem, and the approximate algorithm "L0 Smooting" is used to solve this subproblem.

[0085] Update Lagrange multipliers and It can be expressed as:

[0086]

[0087] To verify the performance of our method with incomplete data, we conducted research on a simulated dataset (using SpekCalc software to generate X-ray spectrum data at 50 kVp, divided into eight energy channels: [16-22) keV, [22-25) keV, [25-28) keV, [28-31) keV, [31-34) keV, [34-37) keV, [37-41) keV, and [41-50) keV). We set the sampling interval to 4 degrees and added low-intensity Gaussian noise to the image. We then selected three channels from the eight-channel CT images for presentation.

[0088] The reconstructed image results of different algorithms under incomplete data problems are as follows Figure 3 The figure shows, from top to bottom, the image reconstruction results of the SART algorithm, the ASD-POCS algorithm, the SISTER algorithm, and the proposed algorithm. It can be directly observed that the SART algorithm has the worst image quality, with severe loss of the object's internal structure. The ASD-POCS algorithm has improved image quality, but the object's interior is still affected by a large amount of noise. Compared with the above two algorithms, the SISTER algorithm significantly improves the results and suppresses a large amount of noise. However, the algorithm is still affected to a certain extent in the fine areas of the object and cannot recover the detailed features of these areas. The results of the proposed method are closest to the true value and can recover most of the image details.

[0089] Figure 4 The image reconstruction results of different algorithms are shown along Figure 3 The dotted line section can be seen from Figure 4 It can be seen from the figure that the profiles of the SART algorithm and the ASD-POCS algorithm fluctuate greatly, and the errors with the true values ​​are also large; the SISTER algorithm obtains better profile results, but still cannot recover well in some edge areas; the method of the present invention obtains the best profile results, with the smallest error with the true value, especially in the edge area, which verifies the effectiveness of the method of the present invention in edge preservation.

[0090] Figure 5 The numerical results of PNSR for images reconstructed by different algorithms are shown. The PSNR values ​​of the proposed method in different channels are as high as 39.7786dB, 39.4527dB and 34.1206dB, which are better than other compared algorithms, indicating that the proposed method has certain advantages in noise suppression.

[0091] To verify the performance of the method of the present invention in low-dose applications, the present invention conducted research on a simulation data set (using SpekCalc software to generate X-ray spectrum data with an energy spectrum of 50 kVp, and dividing it into 8 energy channels: [16-22)keV, [22-25)keV, [25-28)keV, [28-31)keV, [31-34)keV, [34-37)keV, [37-41)keV, and [41-50)keV). This embodiment collects projection data from 140 angles within a 360-degree scanning range and adds high-intensity Gaussian noise to the collected projection data set. The Gaussian noise follows a normal distribution with a mean of 0 and a variance of 0.055.

[0092] The reconstructed image results of different algorithms under low-dose problems are as follows Figure 6 The figure shows, from top to bottom, the image reconstruction results of the SART algorithm, the ASD-POCS algorithm, the SISTER algorithm, and the proposed method. The SART and ASD-POCS algorithms are severely affected by noise and cannot recognize the internal structure of the object. The SISTER algorithm can suppress noise interference to a certain extent, but is still affected by noise in the areas indicated by the arrows. The proposed method restores most of the image details and achieves a higher-precision reconstruction result than other compared algorithms.

[0093] Figure 7 Shows the profiles in different energy spectrum ranges, Figure 7 It can be seen that the method of the present invention obtains a relatively ideal profile result, which is closest to the true value, indicating that the algorithm has certain advantages in suppressing noise.

[0094] Figure 8 Quantitative comparisons of PSNR for reconstruction results under low-dose conditions are presented. The proposed method achieved optimal results across these three evaluation metrics. Compared to the SART algorithm, the proposed method achieved peak signal-to-noise ratios of 37.1523 dB, 37.0246 dB, and 32.7097 dB at energy levels of [16-22) keV, [28-31) keV, and [41-50) keV, respectively, exceeding the PSNR values ​​of other algorithms. These quantitative results further demonstrate the effectiveness of the proposed method in low-dose MECT imaging.

[0095] In terms of the key performance indicators of the algorithm, the iterative characteristics of the algorithm are examined, and the results are as follows Figure 9As shown (the starting point of the curve, from top to bottom, corresponds to: [16-22)keV, [22-25)keV, [25-28)keV, [28-31)keV, [31-34)keV, [34-37)keV, [37-41)keV, and [41-50)keV),) after a certain number of iterations, the RMSE of the reconstruction results at different energy levels of the proposed method converges to a stable and small value. Experimental results verify the effectiveness of the proposed method in spectral CT image reconstruction.

[0096] On the basis of the above embodiments, the present invention further proposes a spectral CT image reconstruction device based on joint regularization, comprising:

[0097] A similar block tensor construction module is used to pre-process the collected multi-channel projection data using a similar block matching operation to obtain a high-dimensional similar block tensor constructed with similar blocks;

[0098] The image reconstruction module is used to extract the low rank of multi-channel images and the sparsity of single-channel images from the extracted high-dimensional similar block tensors using a joint regularization framework, thereby obtaining the reconstructed energy spectrum CT image.

[0099] Furthermore, the similar block tensor construction module is specifically used to: select a noise image under a channel to perform similar image block matching, and extract corresponding similar blocks at the same position under different channels to form a tensor form.

[0100] Furthermore, the image reconstruction module is specifically used to:

[0101] Construct the reconstruction model as follows:

[0102]

[0103] in, represents the estimated reconstructed energy spectrum CT image; p s =Ax s +ε s ,s=1,2,...,S,, S is the total energy level of X-rays, s is its index, represents the projection data collected at the s energy level, h represents the projection data collected at a single energy level; A∈R h×g represents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Indicates the error between the true value and the estimated value; is the data fidelity term; R1(x) represents the weighted tensor nuclear norm regularization, which is used to achieve low-rank characterization of multi-channel images. represents the t-th similar block tensor, t=1,...,T, T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor; R2(x) represents the L0 norm regularization of the image gradient domain, which is used to realize the sparsity characterization of single-channel images. ω and ρ are the weights for balancing the two regularization terms and the fidelity term;

[0104] The constrained reconstruction model is converted into an unconstrained form using the augmented Lagrangian function, and the model is solved using the alternating direction multiplier method.

[0105] In summary, the present invention can effectively characterize the prior characteristics of spectral CT images by introducing image gradient domain L0 norm regularization and weighted tensor nuclear norm regularization, thereby reducing radiation dose and improving imaging efficiency. The feasibility of the present invention has been verified in research experiments on low-dose problems and incomplete data problems.

[0106] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A spectral CT image reconstruction method based on joint regularization, characterized in that: include: Step 1: Preprocess the collected multi-channel projection data using similar block matching operations to obtain a high-dimensional similar block tensor constructed with similar blocks; including: Based on the third-order tensor to describe the energy spectrum image data, for a given third-order tensor Use the weighted tensor nuclear norm to characterize the rank of the tensor: Among them, σ k (x) represents the different principal components U under each module in the tensor χ i The intensity of b k Indicates that each σ k (χ) corresponds to a non-negative weight; Non-negative weights at the l+1th iteration Set to The inverse proportion is expressed as: Among them, c is set to 4e-2; Set to 1e-5 to avoid division by zero; Based on the preprocessing of similar block matching operations, the weighted nuclear norm minimization model is described as: Where T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor; The weighted nuclear norm minimization model is solved using high-order singular value decomposition to obtain an updated third-order tensor. Step 2: For the extracted high-dimensional similarity block tensor, a joint regularization framework is used to extract the low rank of the multi-channel image and the sparsity of the single-channel image, and then the reconstructed spectral CT image is obtained; The step 2 includes: Construct the reconstruction model as follows: in, represents the estimated reconstructed energy spectrum CT image; p s =Ax s +ε s ,s=1,2,...,S,, S is the total energy level of X-rays, s is its index, represents the projection data collected at the s energy level, h represents the projection data collected at a single energy level; A∈R h×g represents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Indicates the error between the true value and the estimated value; is the data fidelity term; R1(x) represents the weighted tensor nuclear norm regularization, which is used to achieve low-rank characterization of multi-channel images. represents the t-th similarity block tensor, t=1,...,T; R2(x) represents the image gradient domain L0 norm regularization, which is used to achieve single-channel image sparsity characterization, ω and ρ are the weights for balancing the two regularization terms and the fidelity term; The constrained reconstruction model is converted into an unconstrained form using the augmented Lagrangian function, and the model is solved using the alternating direction multiplier method.

2. The energy spectrum CT image reconstruction method based on joint regularization according to claim 1, characterized in that: The step 1 includes: selecting a noise image under a channel to perform similar image block matching, and extracting corresponding similar blocks at the same position under different channels to form a tensor form.

3. A spectral CT image reconstruction device based on joint regularization, characterized in that: include: A similar block tensor construction module is used to pre-process the collected multi-channel projection data using similar block matching operations to obtain a high-dimensional similar block tensor constructed with similar blocks; it includes: Based on the third-order tensor to describe the energy spectrum image data, for a given third-order tensor Use the weighted tensor nuclear norm to characterize the rank of the tensor: Among them, σ k (χ) represents the different principal components U under each module in the tensor x i The intensity of b k Indicates that each σ k (χ) corresponds to a non-negative weight; Non-negative weights at the l+1th iteration Set to The inverse proportion is expressed as: Among them, c is set to 4e-2; Set to 1e-5 to avoid division by zero; Based on the preprocessing of similar block matching operations, the weighted nuclear norm minimization model is described as: Where T represents the total number of tensors generated by the block matching operation, and t is the index of the similar block tensor; The weighted nuclear norm minimization model is solved using high-order singular value decomposition to obtain an updated third-order tensor. The image reconstruction module is used to extract the low rank of multi-channel images and the sparsity of single-channel images from the extracted high-dimensional similar block tensors using a joint regularization framework, thereby obtaining the reconstructed spectral CT image. The image reconstruction module is specifically used for: Construct the reconstruction model as follows: in, represents the estimated reconstructed energy spectrum CT image; p s =Ax s +ε s ,s=1,2,...,S,, S is the total energy level of X-rays, s is its index, represents the projection data collected at the s energy level, h represents the projection data collected at a single energy level; A∈R h×g represents the system matrix describing the forward projection process; x s ∈R g represents the CT images under multiple energies to be obtained, and g represents the total number of pixels of the CT image under a single energy; Indicates the error between the true value and the estimated value; is the data fidelity term; R1(x) represents the weighted tensor nuclear norm regularization, which is used to achieve low-rank characterization of multi-channel images. represents the t-th similarity block tensor, t=1,...,T; R2(x) represents the image gradient domain L0 norm regularization, which is used to achieve single-channel image sparsity characterization, ω and ρ are the weights for balancing the two regularization terms and the fidelity term; The constrained reconstruction model is converted into an unconstrained form using the augmented Lagrangian function, and the model is solved using the alternating direction multiplier method.

4. The spectral CT image reconstruction device based on joint regularization according to claim 3, characterized in that: The similar block tensor construction module is specifically used to select a noise image under a channel for similar image block matching, and extract corresponding similar blocks at the same position under different channels to form a tensor form.

Images