An ultrasonic speckle suppression method based on high-order matrix and sparsity joint regularization

Abstract

The application discloses a speckle noise suppression method based on high-order matrix and sparsity joint regularization, and belongs to the technical field of ultrasonic imaging post-processing. The method is as follows: logarithmic compression and interpolation operation are performed on an ultrasonic image; a speckle noise model is constructed; a fidelity term is established; a speckle removal model is established; an optimization solving model is established; the minimum solution is converted into an analytical solution; the constraint problem is converted into an unconstrained problem; and the Lagrange multiplier parameter is updated. The application integrates the steps of logarithmic compression, interpolation, modeling and regularization constraint, can effectively deal with the speckle noise in the ultrasonic image, and provides a comprehensive and effective solution for improving the quality of the ultrasonic image. While effectively removing the noise, the application can effectively protect the edge information of the image and does not introduce noise such as ladder artifacts. Based on the high-order matrix and sparsity joint regularization constraint, the spatial correlation and texture information of the image are more comprehensively considered, so that the denoising process is more accurate and fine.

Description

Technical Field

[0001] This invention relates to an ultrasonic speckle suppression method based on a combination of high-order matrices and sparsity regularization, belonging to the field of ultrasonic imaging post-processing technology. Background Technology

[0002] Ultrasound imaging, as one of the most commonly used forms of medical imaging, is widely used in medical diagnosis due to its advantages of being non-invasive, low-cost, portable, and providing real-time imaging. However, due to coherent interference caused by scattering particles, ultrasound images are often affected by speckle noise, which presents a granular pattern, reducing image contrast and complicating the extraction of important information from speckle-damaged images. Therefore, speckle noise removal has become an important task in processing and analyzing ultrasound imaging signals. However, speckle noise is usually not additive and does not follow a Gaussian normal distribution, making its removal from damaged images even more challenging.

[0003] Current methods for addressing speckle in ultrasound images include local adaptive filters, anisotropic diffusion filters, multi-scale filters, and nonlocal mean filters. While existing speckle suppression methods have improved the image signal-to-noise ratio to some extent, and despite their diverse principles and widespread application, they still suffer from issues such as information loss, poor performance in handling non-uniform speckle noise, and difficulty in processing individual pixels. Even currently used deep learning methods, despite significant achievements in noise removal, still require a large number of calibrated sample images, making them unsuitable for real-world ultrasound images.

[0004] In general, existing speckle removal methods struggle to perfectly preserve edge detail while denoising. This invention aims to overcome these shortcomings and provide a more comprehensive and effective solution for speckle removal in ultrasound images. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention provides an ultrasonic speckle suppression method based on the joint regularization of high-order matrices and sparsity.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an ultrasonic speckle suppression method based on the joint regularization of high-order matrices and sparsity, the method comprising the following steps:

[0007] S1: Establish a speckle removal model;

[0008] S2: Denoising image acquisition.

[0009] Compared with the prior art, the beneficial effects of the present invention are:

[0010] 1. This invention integrates logarithmic compression, interpolation, modeling, and regularization constraints to effectively address speckle noise in ultrasound images, providing a comprehensive and effective solution for improving ultrasound image quality. Furthermore, while effectively removing noise, it effectively preserves the image's edge information and does not introduce noise such as staircase artifacts. Based on high-order matrices and sparse joint regularization constraints, it more comprehensively considers the spatial correlation and texture information of the image, making the denoising process more accurate and refined.

[0011] 2. This invention adopts the Split-Bregman algorithm, combined with an optimized solution model, to achieve efficient solution. It not only has a rapid denoising process, but also maintains the stability of the algorithm, making it more suitable for practical application scenarios of ultrasound image processing.

[0012] 3. This invention does not require changes to the hardware structure of ultrasonic equipment, making it more economical and applicable to various types of ultrasonic equipment. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention;

[0014] Figure 2 This is a simulation comparison analysis diagram of edge information, in which:

[0015] (a) is a noise-free reference image;

[0016] (b) is a noisy image;

[0017] (c) is the image after Lee filtering;

[0018] (d) is the image processed using the present invention;

[0019] Figure 3 These are simulation comparison and analysis diagrams of complex structures, in which:

[0020] (a) is a noise-free reference image;

[0021] (b) is a noisy image;

[0022] (c) is the image after Lee filtering;

[0023] (d) is the image processed using the present invention;

[0024] Figure 4 This is a comparative analysis chart of experimental results, in which:

[0025] (a) is a noise-free reference image;

[0026] (b) is a noisy image;

[0027] (c) is the image after Lee filtering;

[0028] The second row of images shows high-contrast areas.

[0029] The third row of images shows the low-contrast areas. Detailed Implementation

[0030] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0031] An ultrasonic speckle suppression method based on the joint regularization of high-order matrices and sparsity, the method comprising the following steps:

[0032] S1: Establish a speckle removal model;

[0033] S101: Perform beamforming on ultrasound images, along with logarithmic compression and interpolation operations.

[0034] S102: The multiplicative speckle noise distribution problem is transformed into an additive speckle noise distribution problem. Based on the proportional relationship between the mean and variance of speckle noise, the speckle noise model is constructed as follows:

[0035]

[0036] In formula (1):

[0037] g represents an ultrasound image with noise;

[0038] f represents the original image without noise;

[0039] n represents Gaussian noise with zero mean;

[0040] Transforming equation (1), we get:

[0041]

[0042] S103: Based on equation (2), the fidelity term I used to describe the distance between the noise-free original image f and the noisy ultrasound image g is as follows:

[0043]

[0044] S104: High-order matrices are used to constrain the smoothness of noise. These constraints can more comprehensively consider spatial correlation and texture information in the image, thus preserving structural details while suppressing speckle noise. Sparsity-based joint regularization is used to constrain the extensibility of high-frequency information, better capturing subtle changes and features in the image. Combining the fidelity term obtained in S103, the speckle removal model is established as follows:

[0045]

[0046] In equation (4):

[0047] α represents the weighting coefficient for fidelity;

[0048] β represents the sparsity weighting coefficient;

[0049] ||·||1 represents the l1 norm;

[0050] ||·||2 represents the l2 norm;

[0051] R(f) represents a higher-order derivative matrix, and the specific form of the constraint terms is as follows:

[0052]

[0053] in:

[0054] ∫ Ω This represents a summation operation within the range Ω;

[0055] r represents a pixel;

[0056] Ω represents all pixels of f;

[0057] f xx and f xy f yx f yy These represent the directional derivatives corresponding to the direction of the subscript.

[0058] S2: Denoising image acquisition.

[0059] S201: For the non-quadratic function problem of the constraint term in the speckle removal model, the following optimization solution model is established by combining the Split-Bregman algorithm:

[0060]

[0061] S202: Introducing intermediate variable u xx u yy u xy , u and w, such that: u xx =f xx u yy =f yyu xy =2f xy , u=βf, w=f, and the minimum solution of equation (6) is transformed into an analytical solution as follows:

[0062]

[0063] In equation (7):

[0064] Φ(w,u) represents the transpose symbol;

[0065] S203: In order to reduce the complexity of the iterative calculation of equation (7), the Lagrange multiplier is used to iteratively solve equation (7), and finally the constrained problem of equation (7) is transformed into the following unconstrained problem:

[0066]

[0067] In equation (8):

[0068] λ represents the Lagrange multiplier coefficients;

[0069] Representation symbol;

[0070] v xx v xy v yy v and v w All represent parameters of the Lagrange multiplier;

[0071] The optimal solution of equation (8) constitutes the saddle point of the augmented Lagrangian function, which is determined by solving a series of subproblems:

[0072]

[0073] In equation (9):

[0074] w k This represents the k-th iteration of the intermediate variable w;

[0075] u k This represents the k-th iteration of the intermediate variable u;

[0076] f k The k-th iteration represents the original, noise-free image f;

[0077] v k The k-th iteration represents the parameters v of the Lagrange multiplier;

[0078] Then: the result of the (k+1)th iteration of the intermediate variable w is:

[0079]

[0080] definition:

[0081]

[0082] Then the first and second derivatives of G(w) can be obtained as follows:

[0083]

[0084]

[0085] Complete w using Newton's method. k+1 The subproblems are solved as follows:

[0086]

[0087] The series of subproblems are represented as follows:

[0088]

[0089]

[0090]

[0091] S204: Fixed w k+1 and u k+1 Then the subproblem of the noise-free original image f simplifies to:

[0092]

[0093] S205: Solve equation (18) by differentiation and Fourier transform to obtain the predicted value f of the noise-free original image f after the k-th iteration. (k+1) The obtained ultrasound reconstructed image with speckle noise removal is represented by the following iterative solution:

[0094]

[0095]

[0096] In equation (19):

[0097] FFT stands for Fourier;

[0098] iFF stands for Inverse Fourier Transform;

[0099] as well as This represents the second-order derivative operator corresponding to the subscript direction, where: u k , v k u xx u xy uyy u, v xx v xy v yy The predicted value after k iterations of v;

[0100] In equation (20):

[0101] N s This represents the integrated term after the derivative of the k-th iteration;

[0102] Represents N s The predicted value after the kth iteration;

[0103] represent Transpose of;

[0104] S206: Update Lagrange multiplier parameters as follows:

[0105]

[0106] S207: Similarly, we can obtain:

[0107]

[0108]

[0109]

[0110] v k+1 =v k +f k+1 -w k+1 (25).

[0111] This invention, based on the speckle noise distribution characteristics of ultrasound images, transforms the multiplicative noise distribution problem into an additive speckle noise distribution problem with zero mean through a corresponding mathematical model. Based on this, a corresponding fidelity-preserving term is constructed, and combined with a joint regularization term, a method for suppressing ultrasound speckle is proposed. In this invention, the regularization term is represented by a combination of a second-order matrix and a sparse term. The second-order constraint effectively smooths the noise, while the sparse regularization constraint broadens high-frequency information, thus providing well-preserved edge features. Subsequently, to address the issue that the constraint term in the speckle suppression method is not a quadratic function, this invention integrates the fidelity-preserving term and the regularization term, and establishes a corresponding optimization solution model using the Split-Bregman algorithm. By introducing intermediate variables for iterative solution, the method ultimately achieves perfect preservation of edge information in ultrasound images while suppressing noise.

[0112] The image reconstruction effect is closely related to the fidelity weighting coefficient α and the sparsity weighting coefficient β. By adjusting the ratio between the two, we can obtain an image that removes speckle while perfectly preserving edge and detail information.

[0113] Edge simulation results are as follows Figure 2 As shown, it can be observed that, compared with traditional algorithms, the present invention effectively removes noise while better preserving edge segment information.

[0114] To further demonstrate the robustness of the present invention, Figure 3 A more complex structural diagram is provided. As can be seen from the position pointed to by the arrow in the magnified image, compared with traditional algorithms, this invention can better preserve the filamentary structure while effectively removing noise, demonstrating its strong edge and detail preservation capabilities.

[0115] Real ultrasound results such as Figure 4 As shown, the results indicate that, compared with traditional algorithms, the present invention can preserve complete details and edge information while removing noise in both high-contrast and low-contrast regions of the image, consistent with the simulation results.

[0116] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0117] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for suppressing ultrasonic speckle based on the joint regularization of high-order matrices and sparsity, characterized in that: The method includes the following steps: S1: Establish a speckle removal model; S1 includes the following steps: S101: Perform beamforming on ultrasound images, and then perform logarithmic compression and interpolation operations; S102: The multiplicative speckle noise distribution problem is transformed into an additive speckle noise distribution problem, and the speckle noise model is constructed as follows: （1） In formula (1): g represents an ultrasound image with noise; f represents the original image without noise; n represents Gaussian noise with zero mean; Transforming equation (1), we get: （2） S103: Based on equation (2), establish a fidelity term to describe the distance between the noise-free original image f and the noisy ultrasound image g. as follows: （3） S104: By utilizing the high-order matrix to constrain the smoothness of noise, and by utilizing sparsity and joint regularization to constrain the extensibility of high-frequency information, combined with the fidelity term obtained in S103, the speckle removal model is established as follows: （4） In equation (4): Weighting coefficients representing fidelity; Weighting coefficients representing sparsity; represent Norm; represent Norm; R(f) represents a higher-order derivative matrix, and the specific form of the constraint terms is as follows: （5） in: This represents a summation operation within the range Ω; Represents a pixel; Ω represents All pixels; as well as , , These represent the directional derivatives corresponding to the direction of the subscripts; S2: Denoising image acquisition; S2 includes the following steps: S201: For the non-quadratic function problem of the constraint term in the speckle removal model, the following optimization solution model is established by combining the Split-Bregman algorithm: （6） S202: Introducing intermediate variable u xx u yy u xy , u and w, such that: u xx =f xx u yy =f yy u xy =2f xy u= , w=f, and the minimum solution of equation (6) is transformed into an analytical solution as follows: （7） In equation (7): Representation symbol; S203: Using a Lagrange multiplier to iteratively solve equation (7), the constrained problem of equation (7) is finally transformed into the following unconstrained problem: （8） In equation (8): Represents the coefficients of the Lagrange multiplier; Representation symbol; , , , as well as All represent parameters of the Lagrange multiplier; The optimal solution of equation (8) constitutes the saddle point of the augmented Lagrangian function, which is determined by solving a series of subproblems: （9） In equation (9): Representing intermediate variables The k-th iteration; Representing intermediate variables The k-th iteration; Represents the original image without noise. The k-th iteration; Represents the parameters of a Lagrange multiplier The k-th iteration; Then: the result of the (k+1)th iteration of the intermediate variable w is: （10） definition: （11） Then we can obtain The first and second derivatives are as follows: （12） （13） Complete using Newton's method. The subproblems are solved as follows: （14） The series of subproblems are represented as follows: （15） （16） （17） S204: Fixed and Then the subproblem of the noise-free original image f simplifies to: （18） S205: Solve equation (18) by differentiation and Fourier transform to obtain the predicted value of the noise-free original image f after the k-th iteration. The obtained ultrasound reconstructed image with speckle noise removal is represented by the following iterative solution: （19） （20） In equation (19): Represents Fourier; Represents the inverse Fourier transform; , as well as This represents the second-order derivative operator corresponding to the subscript direction, where: , , , , , , , They are respectively , , , , , , , The predicted value after k iterations; In equation (20): This represents the integrated term after the derivative of the k-th iteration; represent The predicted value after the kth iteration; represent Transpose of; S206: Update Lagrange multiplier parameters as follows: （21） S207: Similarly, we can obtain: （22） （23） （24） （25）。

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