Energy spectrum CT reconstruction method and device based on tensor nuclear norm and transformation Lp norm

Abstract

The present invention belongs to the technical field of spectral CT reconstruction, and particularly relates to a spectral CT reconstruction method and device based on tensor nuclear norm and transformation Lp norm, the method comprising selecting a frame set transformation matrix and initializing an image; using block matching technology to establish the correlation within and between channels of the spectral CT image, and constructing a non-local similarity tensor; integrating the non-local similarity tensor into a reconstruction model, and updating the reconstruction model; performing spectral CT reconstruction based on the frame set tensor nuclear norm and transformation Lp norm; and judging whether the quality of the reconstructed image meets the requirements. The present invention uses the frame set tensor nuclear norm to explore the correlation between images of channels, and uses the constructed non-local similarity tensor to improve the objective function, establishes a new reconstruction model, and improves the convergence efficiency and the quality of the reconstructed image through continuous iteration and loop mechanism.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectral CT reconstruction, and in particular relates to a spectral CT reconstruction method and device based on a tensor nuclear norm and a transformation Lp norm. Background Art

[0002] Computed Tomography (CT) as a modern imaging technology has been widely used in medicine, industry and other fields. However, traditional CT technology uses X-rays at a single energy for imaging, and its ability to distinguish material components is limited. In order to break through the imaging limitations of traditional CT technology, spectral CT uses the difference in the attenuation coefficient of a material at different X-ray energies to obtain richer material information. It has the ability to identify and analyze materials that traditional CT technology does not have. As a new imaging technology, it is being gradually studied and used.

[0003] The key step in spectral CT reconstruction is to use the X-ray projection information at multiple energies collected by the detector to restore the distribution of different material information inside the scanned object. It directly determines the imaging quality of spectral CT and affects the analysis, processing and application of subsequent spectral CT reconstruction images. In order to obtain high-quality spectral CT imaging results, how to develop and design efficient spectral CT reconstruction algorithms has become a hot and difficult issue in the current research field of X-ray imaging, and has important research and application value.

[0004] On the one hand, the traditional CT sparse regularization reconstruction method based on the single energy assumption can be directly applied to spectral CT reconstruction. For example, in 2012, Xu et al. applied TV regularization to spectral CT region of interest (ROI) reconstruction; in 2013, Zhao et al. proposed an iterative method based on a tight frame to improve the image quality of spectral CT reconstruction; in 2016, Zeng et al. introduced the concept of structure tensor and transformed the TV regularization method into a penalized weighted least squares method, achieving better results than traditional methods. These methods process each channel image separately, so that each channel image has a strong denoising effect. However, they ignore the high correlation between different channel images of spectral CT, resulting in the degradation of image texture and edges.

[0005] On the other hand, as a way to represent high-dimensional data, tensors can maintain the characteristics of the data itself, so tensor-based methods have gradually played an important role in spectral CT reconstruction. For example, in 2014, Semerci et al. proposed two nuclear norm spectral reconstruction models and algorithms based on the tensor singular value decomposition method. This method can express the similarity between energy spectra based on the nuclear norm and can effectively utilize the data correlation in the energy spectrum domain; in 2015, Li et al. proposed the tensor-based PRISM algorithm and conducted experimental research on dynamic dual-energy data; in 2018, Wu et al. integrated the L0 norm into the tensor dictionary learning (TDL) method and made active attempts in low-dose spectral imaging. In 2019, Zheng et al. proposed the transformation Lp model and conducted model and algorithm research on sparse sampling CT reconstruction.

[0006] The non-local prior method groups similar sub-blocks of the image as basic processing units. It is another powerful tool to utilize the self-similarity of the image and is playing an important role in spectral reconstruction. In 2015, Kim et al. proposed a joint spectral CT reconstruction algorithm based on the low-rank penalty function of the image block to reconstruct artifacts of limited sparse angles in spectral CT. In 2019, Xia et al. jointly designed tensor expressions using the self-similarity of sub-blocks in the image domain and spectral domain, and designed a tensor low-rank decomposition regularization model based on the idea of ​​robust principal component analysis, which has advantages in suppressing image artifacts and maintaining details. Summary of the invention

[0007] In view of the problems existing in the prior art, the present invention proposes a spectral CT reconstruction method and device based on the tensor nuclear norm and the transformation Lp norm, which improves the convergence efficiency and the quality of the reconstructed image.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The present invention provides a spectral CT reconstruction method based on tensor nuclear norm and transformation Lp norm, comprising the following steps:

[0010] Step 1, select the frame set transformation matrix and initialize the image;

[0011] Step 2, using block matching technology to establish the correlation within and between channels of the spectral CT image and construct a non-local similarity tensor;

[0012] Step 3, integrating the non-local similarity tensor of step 2 into the reconstruction model, and updating the reconstruction model;

[0013] Step 4, performing spectral CT reconstruction based on the frame set tensor nuclear norm and the transformed Lp norm;

[0014] Step 5, determine whether the quality of the reconstructed image meets the requirements, if yes, then end, if not, then execute step 2.

[0015] Furthermore, the frame set transformation matrix W and the decomposition level l are selected, and the initial image is an all-0 or all-1 matrix.

[0016] Furthermore, the step 2 specifically includes: firstly, a reference image block p is given i,j , using block matching technology to extract the first channel of the initial image in step 1 i,j There are N similar image blocks in total p and group them into sets of similar image blocks; repeat this operation in different channels, and vectorize different sets of similar image blocks and stack them in the order of channels to form non-local similarity tensors.

[0017] Furthermore, by changing the selected reference image block, different sets of similar image blocks will be obtained.

[0018] Furthermore, the expression for updating the reconstructed model in step 3 is as follows:

[0019]

[0020] In the formula, represents the nonlocal similarity tensor, A represents the system matrix, x s represents the sth channel of the spectral CT image X, that is, the CT image at the sth energy, with a total of S energies; s represents the projection data at the sth energy, represents the gradient image at the sth energy, FTNN represents the frame set tensor nuclear norm, TLp represents the transformation Lp norm, μ represents the non-negative transformation Lp norm penalty factor, and λ represents the frame set tensor nuclear norm penalty factor.

[0021] Furthermore, the calculation formulas for the frame set tensor nuclear norm and the transformation Lp norm are as follows:

[0022]

[0023]

[0024] In the formula, Represents the i-th component of the gradient image arranged in a column vector, with a total of N, where N represents the total number of image pixels; W∈R wS×S represents the frameset transformation matrix, represents the matrix obtained by expanding X modulo-3, and n represents The nth forward slice of fold3 represents the tensor formed by stacking the unfolded matrix modulo -3, a∈(0,+∞), 0 <p≤1。

[0025] Furthermore, the step 4 specifically includes:

[0026] The augmented Lagrange multiplier method is used to update the model in step 3. The expression is as follows:

[0027]

[0028] The above expression can be further rewritten into an unconstrained optimization model as follows:

[0029]

[0030] Where Λ1, Λ2 represent Lagrange multipliers, and ρ1, ρ2 represent non-negative penalty parameters.

[0031] Furthermore, the alternating direction method is used to find the minimum value of the objective function for the unconstrained optimization model. The iterative formula is as follows:

[0032]

[0033] In the formula, Represents the reconstructed image of this round, 0≤ξ≤1.

[0034] Furthermore, the quality of the reconstructed image in step 5 meets the requirements when: there is no significant change between the current round of reconstructed images and the previous round of reconstructed images; when the reconstruction of step 4 is performed for the first time, the previous round of reconstructed images refers to the initial image in step 1.

[0035] The present invention also provides a spectral CT reconstruction device based on tensor nuclear norm and transformation Lp norm, comprising:

[0036] Input image initialization module, used to select frame set transformation matrix and initialize image;

[0037] A non-local similarity tensor building module is used to establish the correlation within and between channels of spectral CT images using block matching technology to construct a non-local similarity tensor;

[0038] A reconstruction model update module is used to incorporate the non-local similarity tensor into the reconstruction model and update the reconstruction model;

[0039] A spectral CT reconstruction module, used for spectral CT reconstruction based on the frame set tensor nuclear norm and the transformation Lp norm;

[0040] The reconstructed image quality judgment module is used to judge whether the quality of the reconstructed image meets the requirements.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] In order to solve the problem that the reconstruction quality of spectral CT images is poor and the decomposition noise further increases, which seriously affects the quality of material decomposition, the present invention proposes a spectral CT reconstruction method based on tensor nuclear norm and transformation Lp norm to achieve high-precision image reconstruction of spectral CT; different from the existing spectral CT reconstruction method based on sparse optimization, the present invention combines the high correlation of images of different channels of spectral CT with gradient sparse prior information, selects appropriate reference image blocks in each round of iteration, extracts similar image blocks, constructs non-local similarity between images between channels, integrates them into the reconstruction model to update the objective function, and performs an iterative strategy based on the alternating direction method on the updated objective function to obtain a higher quality reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 It is a flowchart of a spectral CT reconstruction method based on a tensor nuclear norm and a transformation Lp norm according to an embodiment of the present invention;

[0045] Figure 2 Schematic diagram of the process of constructing a non-local similarity tensor of energy spectrum CT according to an embodiment of the present invention;

[0046] Figure 3 It is a simulation NCAT example diagram of an embodiment of the present invention;

[0047] Figure 4 1 is a diagram of the simulated NCAT reconstruction result of an embodiment of the present invention, wherein (a) represents the reconstruction result under 80 kVp energy, (b) represents the reconstruction result under 100 kVp energy, and (c) represents the reconstruction result under 120 kVp energy. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] like Figure 1 As shown, the energy spectrum CT reconstruction method based on the tensor kernel norm and the transformation Lp norm of this embodiment includes the following steps:

[0050] Step S11, selecting a frame set transformation matrix and initializing an image.

[0051] Specifically, a frameset transformation matrix W and a decomposition level l are selected, and the initial image is an all-0 or all-1 matrix; the frameset transformation matrix W is generated by any one of piecewise cubic B-spline, Haar wavelet and piecewise linear B-spline, and the decomposition level l takes a value between {1, 2, 3, 4, 5}.

[0052] Step S12, using block matching technology to establish the correlation within and between channels of the spectral CT image, and construct a non-local similarity tensor.

[0053] Specifically, Figure 2 As shown, firstly, a reference image block p is given i,j , using block matching technology to extract the first channel of the initial image in step S11 i,j There are N similar image blocks in total p This operation is repeated in different channels, and different sets of similar image blocks are vectorized and stacked in the order of channels to form non-local similarity tensors. If the selected reference image block is changed, different sets of similar image blocks will be obtained.

[0054] Step S13, integrating the non-local similarity tensor of step S12 into the reconstruction model, and updating the reconstruction model, the expression is as follows:

[0055]

[0056] In the formula, represents the nonlocal similarity tensor, A represents the system matrix, x s Represents spectral CT image The s-th channel of , that is, the CT image at the s-th energy, has a total of S energies; s represents the projection data at the sth energy, represents the gradient image at the sth energy, FTNN represents the frame set tensor nuclear norm, TLp represents the transformation Lp norm, μ represents the non-negative transformation Lp norm penalty factor, λ represents the frame set tensor nuclear norm penalty factor, and λ takes a value between 0 and 1.

[0057] The calculation formulas for the frame set tensor nuclear norm and the transformation Lp norm are as follows:

[0058]

[0059]

[0060] In the formula, Represents the i-th component of the gradient image arranged in a column vector, with a total of N, where N represents the total number of image pixels; W∈R wS×S represents the frameset transformation matrix, represents the matrix obtained by expanding X modulo-3, and n represents The nth forward slice of fold3 represents the tensor formed by stacking the unfolded matrix modulo -3, a∈(0,+∞), 0 <p≤1。

[0061] Step S14, performing spectral CT reconstruction based on the frame set tensor nuclear norm and the transformation Lp norm, specifically includes:

[0062] First, the augmented Lagrange multiplier method is used to update the model of step S13, and the expression is as follows:

[0063]

[0064] Then rewrite the above expression into an unconstrained optimization model:

[0065]

[0066] Where Λ1, Λ2 represent Lagrange multipliers, and ρ1, ρ2 represent non-negative penalty parameters.

[0067] Finally, the alternating direction method is used to find the minimum value of the objective function for the above unconstrained optimization model. The iterative formula is as follows:

[0068]

[0069] In the formula, Represents the reconstructed image of this round, 0≤ξ≤1.

[0070] Step S15, determining whether the quality of the reconstructed image meets the requirements, if yes, executing step S16, if no, executing step S12.

[0071] The quality of the reconstructed image meets the requirements when: there is no significant change between the image reconstructed in the current round and the image reconstructed in the previous round; when the reconstruction in step S14 is performed for the first time, the image reconstructed in the previous round refers to the initial image in step S11.

[0072] Step S16, end.

[0073] A specific example is given below to better explain the present invention. The energy spectrum CT reconstruction method comprises the following steps:

[0074] Step S21, selecting a frameset transformation matrix and initializing an image.

[0075] By using the simulated NCAT data given in advance, such as Figure 3As shown, projection data at three energies of 80, 100, and 120 kVp are obtained according to the fan beam scanning setting, and the appropriate frame set transformation matrix W and decomposition level l are selected. The initial image can be an all-0 or all-1 matrix.

[0076] Step S22, using block matching technology to establish the correlation within and between channels of the spectral CT image, and construct a non-local similarity tensor.

[0077] Step S23, integrating the non-local similarity tensor of step 22 into the reconstructed model, and updating the reconstructed model.

[0078] Step S24, performing spectral CT reconstruction based on the frame set tensor nuclear norm and L0 norm.

[0079] Step S25: display the reconstruction result to check whether the reconstruction effect meets the requirements.

[0080] The image quality is mainly evaluated from the following aspects: 1. Whether the geometric artifacts, scattering artifacts, and hardening artifacts of the image are effectively suppressed. 2. Whether the image's ghosting affects or interferes with the identification of image details. 3. Whether the reconstructed resolution level meets the application requirements.

[0081] The energy spectrum CT reconstruction method is used to reconstruct the simulated projection data of the three energy channels. The energy spectrum reconstruction results are shown in Figure 4 shown.

[0082] The present invention uses the framework set tensor nuclear norm to explore the correlation of images between channels, and uses the constructed non-local similarity tensor to improve the objective function, establishes a new reconstruction model, and improves the convergence efficiency and the quality of the reconstructed image through continuous iteration and loop mechanism.

[0083] Corresponding to the above-mentioned energy spectrum CT reconstruction method based on tensor nuclear norm and transformation Lp norm, this embodiment further proposes an energy spectrum CT reconstruction device based on tensor nuclear norm and transformation Lp norm, including:

[0084] Input image initialization module, used to select frame set transformation matrix and initialize image;

[0085] A non-local similarity tensor building module is used to establish the correlation within and between channels of spectral CT images using block matching technology to construct a non-local similarity tensor;

[0086] A reconstruction model update module is used to incorporate the non-local similarity tensor into the reconstruction model and update the reconstruction model;

[0087] A spectral CT reconstruction module, used for spectral CT reconstruction based on the frame set tensor nuclear norm and the transformation Lp norm;

[0088] The reconstructed image quality judgment module is used to judge whether the quality of the reconstructed image meets the requirements.

[0089] It should be noted that, in this article, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus.

[0090] Finally, it should be noted that the above is only a preferred embodiment of the present invention, which is only used to illustrate the technical solution of the present invention, and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A spectral CT reconstruction method based on tensor nuclear norm and transformation Lp norm, characterized in that: The following steps are involved: Step 1, select the frame set transformation matrix and initialize the image; Step 2: Use block matching technology to establish the correlation within and between channels of the spectral CT image and construct a non-local similarity tensor; specifically, it includes: First, given a reference image block p i,j , using block matching technology to extract the first channel of the initial image in step 1 i,j There are N similar image blocks in total p and form a set of similar image blocks; repeat this operation in different channels, and vectorize different sets of similar image blocks and stack them in the order of channels to form a non-local similarity tensor; change the selected reference image block to obtain a different set of similar image blocks; Step 3, incorporate the non-local similarity tensor of step 2 into the reconstruction model and update the reconstruction model; the expression for updating the reconstruction model is as follows: In the formula, represents the nonlocal similarity tensor, A represents the system matrix, x s Represents spectral CT image The s-th channel of , that is, the CT image at the s-th energy, has a total of S energies; s represents the projection data at the sth energy, ▽x s represents the gradient image at the sth energy, FTNN represents the framework set tensor nuclear norm, TL p represents the transformation Lp norm, μ represents the non-negative transformation Lp norm penalty factor, and λ represents the frame set tensor nuclear norm penalty factor; the calculation formulas of the frame set tensor nuclear norm and the transformation Lp norm are as follows: In the formula, ▽x s,i Represents the i-th component of the gradient image arranged in a column vector, with a total of N, where N represents the total number of image pixels; W∈R wS′S represents the frameset transformation matrix, express According to the matrix obtained by modulo-3 expansion, n represents The nth forward slice of fold3 represents the tensor formed by stacking the unfolded matrix modulo-3, a∈(0,+￥), 0 <p￡1; Step 4, performing spectral CT reconstruction based on the frame set tensor nuclear norm and the transformed Lp norm; Step 5, determine whether the quality of the reconstructed image meets the requirements, if yes, then end, if not, then execute step 2.

2. The energy spectrum CT reconstruction method based on tensor nuclear norm and transformation Lp norm according to claim 1 is characterized in that: Select the frame set transformation matrix W and decomposition level l, and the initial image is a matrix of all 0s or all 1s.

3. The energy spectrum CT reconstruction method based on tensor nuclear norm and transformation Lp norm according to claim 1, characterized in that: The step 4 specifically includes: The augmented Lagrange multiplier method is used to update the model in step 3. The expression is as follows: The above expression can be further rewritten into an unconstrained optimization model as follows: Where Λ1, Λ2 represent Lagrange multipliers, and ρ1, ρ2 represent non-negative penalty parameters.

4. The energy spectrum CT reconstruction method based on tensor nuclear norm and transformation Lp norm according to claim 3 is characterized in that: For the unconstrained optimization model, the alternating direction method is used to find the minimum value of the objective function. The iterative formula is as follows: In the formula, Represents the reconstructed image of this round, 0≤ξ≤1.

5. The energy spectrum CT reconstruction method based on tensor nuclear norm and transformation Lp norm according to claim 1, characterized in that: The quality of the reconstructed image in step 5 meets the requirements when: there is no significant change between the reconstructed image in this round and the reconstructed image in the previous round; when the reconstruction in step 4 is performed for the first time, the reconstructed image in the previous round refers to the initial image in step 1.

6. A spectral CT reconstruction device based on tensor nuclear norm and transformation Lp norm, characterized in that: The device is used to implement the energy spectrum CT reconstruction method based on the tensor nuclear norm and the transformation Lp norm as claimed in any one of claims 1 to 5, the device comprising: Input image initialization module, used to select frame set transformation matrix and initialize image; A non-local similarity tensor building module is used to establish the correlation within and between channels of spectral CT images using block matching technology to construct a non-local similarity tensor; A reconstruction model update module is used to incorporate the non-local similarity tensor into the reconstruction model and update the reconstruction model; A spectral CT reconstruction module, used for spectral CT reconstruction based on the frame set tensor nuclear norm and the transformation Lp norm; The reconstructed image quality judgment module is used to judge whether the quality of the reconstructed image meets the requirements.

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