A low-dose CT image denoising method

Abstract

The present application belongs to the technical field of image denoising, and particularly relates to a low-dose CT image denoising method. The low-dose CT scanning technology can effectively reduce the radiation received by the patient, but at the same time, it also leads to the reduction of the image quality, especially the strip noise in the image, which brings not small challenge to the denoising work. In view of this problem, the present application firstly uses the weighted kernel norm minimization to preliminarily denoise the image and remove the speckle noise; then the preliminarily denoised image is rotated, a direction total variation regularization term is introduced, and a low-rank method is combined to extract the stripe artifact noise; then the preliminarily denoised image is subtracted from the image after the inverse transformation of the rotated image with the stripe artifact noise, and the final denoising result is obtained. The experimental results show that the algorithm can effectively remove the strip noise of the low-dose CT image, and better preserve the image details.

Description

Technical Field

[0001] This invention belongs to the field of image denoising technology, specifically relating to a low-dose CT image denoising method. Background Technology

[0002] Computed tomography (CT) is an imaging modality that has become widely used in recent years. With the increasing prevalence of CT scans in various clinical fields, the potential radiation hazards they pose to the human body have garnered more attention. Compared to other radiological diagnostic tools, CT scans generally involve higher levels of X-ray radiation; therefore, low-dose CT (LDCT) technology is receiving increasing attention. On the one hand, LDCT technology reduces the risks to patients; on the other hand, it also brings new problems. Low-dose scanning protocols (such as reducing tube current) often cause degradation in reconstructed images, leading to the formation of streak artifacts. Artifacts typically have relatively prominent intensity characteristics, which can significantly reduce the ability to distinguish normal or pathological tissues. Moreover, non-uniform noise in CT images obtained through low-dose scanning protocols is often difficult to model. Therefore, improving image denoising algorithms to effectively reduce the interference of noise and artifacts on the original image, enhance visual effects, and improve image quality remains a significant area of ​​research.

[0003] CT image processing is mainly divided into three categories: projection domain data processing, image reconstruction process processing, and post-processing methods for reconstructed images. Since projection domain data processing and image reconstruction algorithms heavily rely on medical clinical data, which is often difficult to obtain, post-processing of the reconstructed images remains a popular practice. In recent years, many excellent algorithms have emerged, such as the NLM algorithm, low-rank matrix approximation, BM3D algorithm, sparse representation, morphological methods, and the increasingly popular deep learning methods, all demonstrating excellent performance in medical image denoising.

[0004] Low-rank matrix approximation methods can generally be divided into two categories: Low-Rank Matrix Factorization (LRMF) methods and Nuclear Norm Minimization (NNM) methods. The goal of LRMF is to find a matrix X that approximates the data matrix Y to be processed as closely as possible, while also being decomposable into the product of two low-rank matrices. However, LRMF suffers from non-convex optimization problems and lacks adaptability. Another research direction in low-rank matrix approximation is NNM. NNM aims to approximate Y with X while minimizing the nuclear norm of X. A significant advantage of NNM is that it is the most compact convex relaxation of a non-convex LRMF problem with a certain data fidelity term. However, NNM methods shrink each singular value to the same degree, which is inconsistent with people's prior knowledge of images. Gu et al. proposed a weighted nuclear norm minimization model (WNNM), which improved the threshold shrinkage part by assigning different weights to the importance of components and shrinking different singular values ​​to different degrees, further improving the algorithm's performance and achieving superior results in image denoising. Xu's adaptive image denoising proposed using weighted nuclear norms has also been successful. Yair's improved method, based on the weighted nuclear norm, demonstrates superior performance in image inpainting by introducing a new regularization term. While low-rank theory exhibits strong performance in removing Gaussian noise, it is less effective at removing non-uniform noise in low-dose CT images, often leaving bar artifacts. This is because bar artifacts in low-dose X-CT images have significant directional information, making them difficult to distinguish from attenuated and degraded tissue structure information.

[0005] To address this problem, this invention proposes a two-stage denoising method that effectively removes stripe noise. This method utilizes low-rank characteristics to divide the noise into two layers: one layer is speckle noise without low-rank characteristics, and the other layer is stripe noise with structural texture characteristics, considered to possess rotational ultra-low-rank properties. Then, based on the different characteristics of the two noise layers, denoising is performed separately. Experiments using simulated and clinical data have shown that the proposed method has good denoising performance. Summary of the Invention

[0006] To effectively remove complex noise from low-dose CT images, a two-step denoising algorithm is proposed. First, the noise is divided into two layers: speckle noise and stripe noise. Since speckle noise lacks low-rank properties, the WNNM algorithm is chosen to remove it, leveraging the low-rank characteristics of the image and stripe artifacts. The WNNM algorithm effectively removes speckle noise without losing too much detail, while retaining strong, directional stripe noise. Therefore, after the first step of denoising with WNNM, the image mainly contains stripe noise. Stripe noise is structural and directional, and when rotated to the vertical direction, the stripe artifacts exhibit ultra-low-rank characteristics. Furthermore, vertical stripe artifacts have a significant impact on the horizontal gradient but a minimal impact on the vertical gradient. Therefore, the second step rotates the initially denoised image, introducing a total variational regularization term and combining it with low-rank constraints to extract stripe noise in the transform domain. Then, the image after subtracting the stripe noise from the initially denoised image and performing an inverse rotation transform yields the final denoised result.

[0007] To achieve the above objectives, the present invention employs the following technical solutions:

[0008] A method for denoising low-dose CT images includes the following steps:

[0009] Step 1: The noise in the low-dose CT image is divided into two layers: one layer is speckle noise without low-rank characteristics, and the other layer is stripe noise with structural texture characteristics, which is considered to have rotational low-rank characteristics.

[0010] Step 2: Use the weighted nuclear norm minimization algorithm to remove speckle noise and obtain a preliminary denoised image;

[0011] Step 3: Rotate the initially denoised image, introduce a total variational regularization term, and then use a low-rank method to extract the stripe noise in the transform domain to obtain the rotated stripe artifact image.

[0012] Step 4: Perform an inverse rotation transformation on the rotated bar artifact image. Subtract the bar noise image after the inverse rotation transformation from the image after the initial denoising to obtain the final denoised image.

[0013] Furthermore, in step 2, the weighted nuclear norm minimization algorithm is used to remove speckle noise to obtain a preliminary denoised image. The specific steps are as follows:

[0014] Step 2.1, for an image block y in a low-dose CT image Y j y j ∈Y, first in image patch y jSearch for similar blocks within a non-local range, rearrange each similar block into a column vector, and then combine all column vectors to obtain the similar block group matrix Y. j We obtain the following equation:

[0015] Y j =X j +N j (1)

[0016] Among them, Y j Let X be a noisy image matrix. j It is Y j The approximate low-rank matrix, i.e., the recovered image matrix, N j This is the noise matrix;

[0017] Step 2.2: Estimate X using the weighted nuclear norm minimization algorithm. j The following optimized formula is obtained:

[0018]

[0019] ||X j || ω,* =∑ i ω i λ i (X j )

[0020] in, For X j An approximate estimate, ||·|| F Let ||X| denote the F-norm of the matrix. j || w,* Represents matrix X j The weighted nuclear norm, λ i (X j ) is matrix X j The i-th singular value. Let ω be the variance of the noisy image Y, and β be the coefficients. ω = [ω1, ω2, ..., ω n ](ω i (≥0) is the weight vector. According to singular value correlation theory, the larger the singular value, the more important its corresponding component. Therefore, the larger the singular value, the smaller its contraction should be, that is, it should be inversely proportional to the singular value, as defined below:

[0021] ω i =C / (λ) i (X j )+ε) (3)

[0022] in, c is a non-zero positive integer, and m is the number of similar blocks, i.e., matrix X. j The number of columns, ε is a small positive constant factor;

[0023] Since the initial λ i (X j Since this cannot be obtained, it is assumed that the speckle noise is uniformly distributed in the two basis spaces U and V, thus obtaining λ. i (X j The estimated initial values ​​are as follows:

[0024]

[0025] Where, λ i (Y j ) is matrix Y j The i-th singular value, where n represents the matrix Y. j The number of rows, i.e. the number of pixels in each image patch that makes up the low-rank matrix;

[0026] The global solution is obtained as follows:

[0027]

[0028] Among them, Y j =UΣV T It is matrix Y j Singular value decomposition, S ω (Σ) represents different degrees of soft thresholding shrinkage of singular values, as follows:

[0029] S ω (Σ) ii =max(Σ ii -ω i ,0) (6)

[0030] Where Σ is a diagonal matrix, Σ ii Let S be the diagonal element of matrix Σ in the i-th row and i-th column. ω (Σ) ii Let matrix S ω (Σ) The diagonal element in the i-th row and i-th column, ω i This is the i-th weight coefficient;

[0031] Step 2.3: Perform steps 2.1 to 2.2 on all image blocks in the noisy image Y, and then aggregate all the processed image blocks together to obtain a preliminary denoised image.

[0032] Furthermore, in step 3, the initially denoised image is rotated, and a total variational regularization term is introduced. Combined with a low-rank method, stripe noise is extracted in the transform domain to obtain the rotated stripe artifact image. The specific steps are as follows:

[0033] Step 3.1: Since the image after initial denoising only contains stripe noise, the image after initial denoising is considered as two layers, represented as follows:

[0034] I = X + R (7)

[0035] Where I represents the image after initial denoising, X represents the clean image, and R represents the stripe noise image;

[0036] Step 3.2, rotate the initially denoised image I, and formula (7) becomes:

[0037]

[0038] Where τ is the rotation operator, X' is the clean image after rotation, and R' is the stripe noise image after rotation;

[0039] Step 3.3: Due to the inherent structure and directionality of stripe noise, it exhibits low rank. After this rotation, the direction of the stripe noise image R' in the rotated image is mainly concentrated in the vertical direction. Therefore, the rank of component R' is extremely small, much lower than the rank of the image to be recovered, X'. Since the rank of stripe noise is much lower than that of the low-dose CT image itself, the method of utilizing the extremely low rank of stripe artifacts can be used again to recover the stripe noise image R'. The final denoised image X is obtained by subtracting the components. Furthermore, stripes themselves have obvious directional characteristics. After rotation, the directionality of the stripe artifact R' in the transform domain is mainly concentrated in the vertical direction, meaning the gradient direction of the stripe artifact is mainly concentrated in the horizontal direction. Therefore, the total directional component is introduced as a constraint term, resulting in the overall low-rank rotation model:

[0040]

[0041] Where λ and ρ are constraint coefficients, ▽ x ,▽ y These represent the derivative operators in the horizontal and vertical directions, respectively. * This represents the nuclear norm.

[0042] Step 3.4: Obtain R', i.e., the rotated bar artifact image, through alternating iterations.

[0043] Furthermore, the specific steps for obtaining R' through alternating iterations are as follows:

[0044] Linearize equation (9) around the current estimate:

[0045]

[0046] Where ▽I is the Jacobian matrix of the initially denoised image I after rotation transformation with respect to the rotation parameter. The non-convex optimization problem of formula (9) is transformed into the following convex optimization problem:

[0047]

[0048] Formula (11) is transformed into three minimization subproblems through alternating minimization:

[0049] Update R': Stripe noise estimation: Based on Lagrange multiplier theory, the constrained convex optimization problem is transformed into an unconstrained convex optimization problem:

[0050]

[0051] Where J is a Lagrange multiplier and α is a constant, Equation (12) is solved by the singular value shrinkage algorithm;

[0052] Update X': Image estimation after rotation:

[0053]

[0054] Where J is a Lagrange multiplier and α is a constant, Equation (13) is solved by the ADMM algorithm and the singular value shrinkage algorithm;

[0055] Update Δτ:

[0056]

[0057] Formula (14) is solved using the TILT algorithm;

[0058] By iteratively updating R' and X' as described above, stripe noise can be removed.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] This method first divides the noise in low-dose CT images into two layers based on the characteristics of the noise: speckle noise, which lacks low-rank property and is denoised using low-rank properties; and stripe artifact noise, which, due to its strong structure and directionality, can be considered low-rank and is also denoised using low-rank properties. However, this method utilizes the fact that the stripe artifacts in the rotated image have a much lower rank than the low-dose CT image itself, applying low-rank constraints to the stripe artifacts to recover the stripe noise image. Then, the stripe artifacts after the inverse rotation transformation are subtracted from the denoising result of the first stage to obtain the final denoised image. To verify the effectiveness of this method, experiments were conducted on both simulated and clinical data. The experimental results show that the proposed algorithm improves the visual effect, especially in terms of detail; it also significantly improves the objective indicators. Attached Figure Description

[0061] Figure 1 A flowchart of a low-dose CT image denoising method;

[0062] Figure 2 These are before-and-after comparison images of the initial noise reduction process;

[0063] Figure 3 This is the final denoised image;

[0064] Figure 4 Diagram of the pelvis;

[0065] Figure 5 This is a clinical chest image;

[0066] Figure 6 A magnified view of the region of interest. Detailed Implementation

[0067] Example 1

[0068] like Figure 1 As shown, a low-dose CT image denoising method of the present invention includes the following steps:

[0069] Step 1: The noise in the low-dose CT image is divided into two layers: one layer is speckle noise without low-rank characteristics, and the other layer is stripe noise with structural texture characteristics, which is considered to have rotational low-rank characteristics.

[0070] Step 2: Use the weighted nuclear norm minimization algorithm to remove speckle noise and obtain a preliminary denoised image. The specific steps are as follows:

[0071] Step 2.1, for an image block y in a low-dose CT image Y j y j ∈Y, first in image patch y j Search for similar blocks within a non-local range, rearrange each similar block into a column vector, and then combine all column vectors to obtain the similar block group matrix Y. j We obtain the following equation:

[0072] Y j =X j +N j (1)

[0073] Among them, Y j Let X be a noisy image matrix. j It is Y j The approximate low-rank matrix, i.e., the recovered image matrix, N j This is the noise matrix;

[0074] Step 2.2: Estimate X using the weighted nuclear norm minimization algorithm. jThe following optimized formula is obtained:

[0075]

[0076] ||X j || ω,* =∑ i ω i λ i (X j )

[0077] in, For X j An approximate estimate, ||·|| F Let ||X| denote the F-norm of the matrix. j || w,* Represents matrix X j The weighted nuclear norm, λ i (X j ) is matrix X j The i-th singular value, Let ω be the variance of the noisy image Y, β be the coefficients, and ω = [ω1, ω2, ..., ω]. n ](ω i (≥0) is the weight vector, defined as follows:

[0078] ω i =C / (λ) i (X j )+ε) (3)

[0079] in, c is a non-zero positive integer, and m is the number of similar blocks, i.e., matrix X. j The number of columns, ε is a small positive constant factor;

[0080] Assuming the speckle noise is uniformly distributed in the two basis spaces U and V, we obtain λ i (X j The estimated initial values ​​are as follows:

[0081]

[0082] Where, λ i (Y j ) is matrix Y j The i-th singular value; n represents the matrix Y j The number of rows, i.e. the number of pixels in each image patch that makes up the low-rank matrix;

[0083] The global solution is obtained as follows:

[0084]

[0085] Among them, Y j =UΣVT It is matrix Y j Singular value decomposition, S ω (Σ) represents different degrees of soft thresholding shrinkage of singular values, as follows:

[0086] S ω (Σ) ii =max(Σ ii -ω i ,0) (6)

[0087] Where Σ is a diagonal matrix, Σ ii Let S be the diagonal element of matrix Σ in the i-th row and i-th column. ω (Σ) ii Let matrix S ω (Σ) The diagonal element in the i-th row and i-th column, ω i This is the i-th weight coefficient;

[0088] Step 2.3: Perform steps 2.1 to 2.2 on all image blocks in the noisy image Y, and then aggregate all the processed image blocks together to obtain a preliminary denoised image.

[0089] Figure 2 The images show a comparison before and after the initial denoising process. (a) is the noisy image, and (b) is the image obtained by denoising the improved Shepp-Logan image using the WNNM algorithm. It can be seen that many stripe noises still exist in the images, indicating that the WNNM algorithm can effectively remove speckle noise in LDCT images, but it cannot effectively remove stripe noise. Since the image after initial denoising mainly contains stripe noise, the next step in this invention is to address the stripe noise.

[0090] Step 3: Rotate the initially denoised image, introduce a total variational regularization term, and then use a low-rank method to extract the stripe noise in the transform domain to obtain the rotated stripe artifact image. The specific steps are as follows:

[0091] Step 3.1, the initially denoised image is considered as two layers, represented as follows:

[0092] I = X + R (7)

[0093] Where I represents the image after initial denoising, X represents the clean image, and R represents the stripe noise image;

[0094] Step 3.2, rotate the initially denoised image I, and formula (7) becomes:

[0095]

[0096] Where τ is the rotation operator, X' is the clean image after rotation, and R' is the stripe noise image after rotation;

[0097] Step 3.3: Remove image information from the transform domain, and by introducing the total directional variation as a constraint term, obtain the overall rotational low-rank model:

[0098]

[0099] Where λ and ρ are constraint coefficients, ▽ x ,▽ y Let ||·|| represent the derivative operators in the horizontal and vertical directions, respectively. * Represents the nuclear norm;

[0100] Step 3.4: Obtain R', i.e., the rotated bar artifact image, through alternating iterations.

[0101] Solving (9) is difficult because the constraint part in formula (9) is nonlinear. Linearizing formula (9) around the current estimate is necessary:

[0102]

[0103] Where ▽I is the Jacobian matrix of the initially denoised image I after rotation transformation with respect to the rotation parameter. The non-convex optimization problem of formula (9) is transformed into the following convex optimization problem:

[0104]

[0105] Formula (11) is transformed into three minimization subproblems through alternating minimization:

[0106] According to the Lagrange multiplier theory, the constrained convex optimization problem is transformed into an unconstrained convex optimization problem:

[0107]

[0108] Where J is a Lagrange multiplier and α is a constant, Equation (12) is solved by the singular value shrinkage algorithm;

[0109] Update X': Denoising image estimation after rotation:

[0110]

[0111] Where J is a Lagrange multiplier and α is a constant, Equation (13) is solved by the ADMM algorithm and the singular value shrinkage algorithm;

[0112] Update Δτ:

[0113]

[0114] Formula (14) is solved using the TILT algorithm;

[0115] R' is obtained through the above iterative updates, thus realizing the extraction of stripe noise.

[0116] Figure 3 The final denoised image is Figure 2 (b) The image after stripe noise removal, compared with Figure 2 Compared with (b), the final denoised image not only removes stripe noise very well, but also does not lose too much detail, indicating that the proposed method for removing stripe noise is effective.

[0117] Example 2

[0118] In this embodiment, the performance of the proposed method is evaluated through experiments with simulated data and real data. Figure 4 (a) shows the simulated pelvic data. Figure 4 (b) is the corresponding LDCT image, which was reconstructed from an analog noise sine curve using an FBP with a Hanning filter (cutoff frequency equal to 80% of the Nyquist frequency). Figure 4 (c), (d), (e), and (f) respectively show the corresponding BM3D image, WNNM image, TLR image, and image of this method.

[0119] In the experiment, the actual data came from an anatomical model of the human chest and torso. CT images were obtained from the chest model using a multi-detector Siemens Somatom Sensation 16CT scanner at a tube voltage of 120 kVp. The raw high-dose CT (HDCT) images were acquired at a higher tube current of 240 mA. Figure 5 Image (a) shows an HDCT image processed by the artifact suppression large-scale nonlocal means (AS-LNLM) method, which demonstrates better performance than the original HDCT image. Therefore, this invention... Figure 5 Image (a) is a reference image. Figure 5 (b) shows an LDCT image obtained with a tube current reduction of 30 mA. Figure 5 Images (c), (d), (e), and (f) respectively show the BM3D image, WNNM image, TLR image, and the image from this method.

[0120] 1. Evaluation Indicators

[0121] In terms of objective metrics, PSNR and SSIM are used as parameters to evaluate the denoising effect. Their expressions are as follows:

[0122] PSNR = 10log 10 (2552 / MSE) (14)

[0123] Where MSE is the mean squared error;

[0124]

[0125] Where, μ x μ y Let x and y be the means of x and y, respectively. Let be the variances of x and y, respectively, and σ be the variances of x and y. xy For covariance, c1 and c2 are two limiting parameters.

[0126] 2. Simulated data experiment

[0127] This section uses simulated low-dose CT images of the pelvis to validate the algorithm's performance. Figure 4 This paper compares the proposed method with algorithms such as BM3D, WNNM, and TLR, which simulate pelvic bone images. Visually, the proposed method shows the best denoising effect, followed by WNNM. However, by observing the area indicated by the arrow, it can be seen that WNNM still exhibits artifacts, while the artifacts are still quite noticeable after denoising by BM3D and TLR. Furthermore, Table 1 shows the PSNR and SSIM indices of two images under various algorithms. It can be seen that the proposed method significantly outperforms the other algorithms in both indices, achieving substantial improvements and verifying the effectiveness of the proposed method.

[0128] Table 1. Simulation Data and Experimental Results

[0129]

[0130] 3. Actual clinical data experiments

[0131] To further validate the performance of the proposed method, experiments were also conducted using clinical data. Figure 5 As can be seen, the algorithm also performs very well on clinical data, not only filtering out bar artifacts but also preserving good edge structure. To more clearly observe the denoising effect, information from locally relevant images was also extracted. Figure 5 The part in box (a) is from Figure 6 As can be seen, after denoising using the method of this invention, the stripe noise is almost invisible, while other methods still show relatively obvious stripe noise. Considering the PSNR and SSIM data given in Table 2, the proposed method remains optimal, achieving a significant improvement, indicating that the proposed method is also effective for clinical data.

[0132] Table 2 Clinical Data and Experimental Results

[0133]

[0134] In summary, this invention first divides noise into two layers based on the characteristics of noise in low-dose CT images: one layer is speckle noise, which lacks low-rank property; the first stage utilizes the low-rank property of the image and stripe artifacts to remove speckle noise. The second layer is stripe artifact noise, which, due to its structural and directional properties, can be considered to have low-rank property; this layer also utilizes low-rank property for denoising. However, here, the stripe artifacts in the rotated image have a much lower rank than the low-dose CT image itself; low-rank constraints are applied to the stripe artifacts to recover the stripe noise image. Then, the stripe artifacts after the inverse rotation transformation are subtracted from the denoising result of the first stage to obtain the final denoised image. To verify the effectiveness of this method, experiments were conducted not only on simulated data but also on clinical data. The experimental results show that the proposed algorithm improves visual performance, especially in terms of detail; it also significantly improves objective indicators.

Claims

1. A method for denoising low-dose CT images, characterized in that, Includes the following steps: Step 1: The noise in the low-dose CT image is divided into two layers: one layer is speckle noise without low-rank characteristics, and the other layer is stripe noise with structural texture characteristics, which is considered to have rotational low-rank characteristics. Step 2: Use the weighted nuclear norm minimization algorithm to remove speckle noise and obtain a preliminary denoised image; Step 3: Rotate the initially denoised image, introduce a total variational regularization term, and then use a low-rank method to extract the stripe noise in the transform domain to obtain the rotated stripe artifact image. Step 4: Perform an inverse rotation transformation on the rotated bar artifact image, and subtract the inverse rotation transformed bar artifact image from the initially denoised image to obtain the final denoised image. In step 3, the initially denoised image is rotated, and a total variational regularization term is introduced. Combined with a low-rank method, stripe noise is extracted in the transform domain to obtain the rotated stripe artifact image. The specific steps are as follows: Step 3.1, the initially denoised image is considered as two layers, represented as follows: （7） in, For the initial denoising of the image, For a clean image, Represents a striped noise image; Step 3.2, the image after initial denoising. After rotational transformation, formula (7) becomes: （8） in, For rotation operators, The clean image after rotation. The image shows the striped noise after rotation; Step 3.3: Remove image information from the transform domain, and by introducing the total directional variation as a constraint term, obtain the overall rotational low-rank model: （9） in, , For constraint coefficients, , Let these represent the derivative operators in the horizontal and vertical directions, respectively. Represents the nuclear norm; Step 3.4, obtain through alternating iterations That is, the rotated bar artifact image; The alternating iterations are obtained , The specific steps are as follows: Linearize equation (9) around the current estimate: （10） in, This is a preliminary denoising image. After the rotation transformation, for the Jacobian matrix of the rotation parameters, the non-convex optimization problem of formula (9) is transformed into the following convex optimization problem: （11） Formula (11) is transformed into three minimization subproblems through alternating minimization: renew Stripe noise estimation: Based on Lagrange multiplier theory, the constrained convex optimization problem is transformed into an unconstrained convex optimization problem. （12） in, It is a Lagrange multiplier. It is a constant, and formula (12) is solved by the singular value shrinkage algorithm; renew Denoising image estimation after rotation: （13） in, It is a Lagrange multiplier. It is a constant, and formula (13) is solved by the ADMM algorithm and the singular value shrinkage algorithm; renew : （14） Formula (14) is solved using the TILT algorithm; The above iterative updates are obtained. This achieves the removal of stripe noise.

2. The low-dose CT image denoising method according to claim 1, characterized in that, In step 2, the weighted nuclear norm minimization algorithm is used to remove speckle noise to obtain a preliminary denoised image. The specific steps are as follows: Step 2.1, for low-dose CT images An image patch , First in the image block The algorithm searches for similar blocks within a non-local range, rearranges each similar block into a column vector, and then combines all column vectors to obtain a similar block group matrix. We obtain the following equation: （1） in, For a noisy image matrix, yes The approximate low-rank matrix, i.e., the recovered image matrix, This is the noise matrix; Step 2.2: Use the weighted nuclear norm minimization algorithm to estimate The following optimized formula is obtained: （2） ； in, for An approximate estimate, Denotes the F-norm of a matrix. Representation matrix The weighted nuclear norm, It is a matrix The A singular value, For noisy images variance For coefficients, It is a weight vector. The definition is as follows: （3） in, , It is a non-zero positive number. The number of similar blocks, i.e., the matrix The number of columns, It is a small positive constant factor; Assuming the speckle noise is uniformly distributed in the two basis spaces U and V, we obtain The estimated initial values ​​are as follows: （4） in, It is a matrix The One singular value; For noisy images variance Representation matrix The number of rows, i.e. the number of pixels in each image patch that makes up the low-rank matrix; The global solution is obtained as follows: （5） in, It is a matrix Singular value decomposition, This involves applying soft thresholding to singular values ​​to varying degrees, as follows: （6） in, It is a diagonal matrix. For matrix No. Line 1 The diagonal elements of the column, For matrix No. Line 1 The diagonal elements of the column, For the first Each weighting coefficient; Step 2.3, for noisy images All image blocks are processed through steps 2.1 and 2.2, and then all processed image blocks are aggregated together to obtain a preliminary denoised image. .

Images