Non-smooth OCT denoising method fusing efficient diffusion sampling prior

Abstract

This invention proposes a non-smooth OCT denoising method that integrates efficient diffusion sampling priors. The method includes: representing the degraded OCT observation image as a Gamma distribution; constructing a data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution; constructing a diffusion denoising prior through implicit inverse diffusion sampling using a pre-trained unconditional fractional diffusion model; combining the data fidelity term for nonlinear speckle suppression with the diffusion denoising prior to construct a non-smooth function; optimizing the non-smooth function using the Bregman iterative algorithm; and outputting the final iteratively obtained image estimate as the optimal solution of the non-smooth function to obtain the final speckle-free OCT image. This invention accelerates the generation speed of fidelity-constrained diffusion by accelerating sampling, and it not only integrates fast sampling priors but also solves the non-smoothness problem caused by fast sampling.

Description

Technical Field

[0001] This invention relates to the field of OCT image denoising, and particularly to a non-smooth OCT denoising method that incorporates efficient diffusion sampling priors. Background Technology

[0002] Speckle suppression in optical coherence tomography (OCT) can be formulated as a class of nonlinear inverse problems. Although diffusion models have made significant progress recently as solvers for such inverse problems, mainstream research remains limited to handling simple linear inverse problems through computationally intensive iterative Markov chains.

[0003] OCT (Optical Coherence Tomography) is an important imaging technique in ophthalmic clinical analysis, providing crucial information for the diagnosis of glaucoma, retinal diseases, and other conditions. However, the speckle noise inherent in coherent imaging systems can significantly degrade image quality, thus hindering clinical analysis. Therefore, speckle suppression in OCT images is essential for clinical applications.

[0004] Speckle suppression is typically much more computationally demanding than linear inverse problems and is prone to converging to local optima. In image restoration, traditional methods for solving inverse problems have historically relied on mathematical modeling, usually constructing an objective function that includes data fidelity terms and regularization terms. Regularization primarily addresses the ill-conditioning of the problem by introducing appropriate prior terms, ultimately leading to the optimal solution. Traditional speckle suppression techniques in OCT images also follow this paradigm; carefully designed prior terms can produce good speckle removal results. However, a significant limitation of these methods is their tendency to produce oversmoothing effects, which often obscure subtle but crucial pathological structures, thus impairing their practical value in clinical OCT analysis.

[0005] Recent research has moved beyond model-based prior methods, incorporating data-driven prior information. Notably, generative diffusion models have advanced inverse problem solving by transforming noise into a learning process that converts it into samples of complex data distributions. Generally, diffusion model-based inverse problem solvers can be categorized into two paradigms: the first paradigm develops task-specific conditional models to achieve superior performance on specific inverse problems. Therefore, its applicability is limited to the specific task at which it was trained. In contrast, the second paradigm emphasizes flexibility, leveraging pre-trained, task-agnostic models to solve general inverse problems within a plug-and-play Bayesian framework. These methods exhibit strong generalization and versatility, adapting to various inverse problem tasks without retraining the diffusion model. However, most of these methods are currently limited to linear inverse problems; effectively extending them to nonlinear cases remains a challenge to be overcome.

[0006] To address this challenge, existing technologies utilize diffusion posterior sampling (DPS) as an efficient method to solve the general nonlinear inverse problem. While promising, DPS has two main limitations in OCT speckle suppression: First, DPS relies on expected values ​​to estimate the initial restored image, but the data distribution of real OCT images is complex, leading to inaccurate estimation. Second, its iterative inverse process involves computational redundancy, making it difficult to meet the practical needs of clinical deployment. Summary of the Invention

[0007] In view of the above situation, the main objective of this invention is to propose a non-smooth OCT denoising method that integrates efficient diffusion sampling priors in order to solve the above-mentioned technical problems.

[0008] This invention proposes a non-smooth OCT denoising method that integrates efficient diffusion sampling priors, the method comprising the following steps:

[0009] Step 1: Acquire degraded OCT observation images; characterize the degraded OCT observation images as a Gamma distribution; construct a data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution;

[0010] Step 2: Using a pre-trained unconditional fractional diffusion model, a diffusion denoising prior is constructed through implicit reverse diffusion sampling;

[0011] Step 3: Combine the data fidelity term of nonlinear speckle suppression with the diffusion denoising prior to construct a non-smooth function;

[0012] Step 4: Initialize the image estimates and intermediate variable values, and use the Bregman iterative algorithm to optimize the solution of the non-smooth function. By initializing the image estimates and the degraded OCT observation image, update the intermediate variable values ​​to obtain the updated intermediate variable values.

[0013] Step 5: Using the updated intermediate variable values ​​as constraints, solve the denoising subproblem dominated by the diffusion denoising prior to obtain the updated image estimate.

[0014] Step 6: Repeat steps 4 and 5 iteratively. When the number of iterations reaches the preset maximum number of iterations, and the difference between the image estimates obtained from two adjacent iterations is less than a preset threshold, output the image estimate obtained from the final iteration as the optimal solution of the non-smooth function to obtain the final speckle-free OCT image.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] 1. This invention accelerates the generation speed of fidelity term constraint diffusion by accelerating sampling. It not only integrates fast sampling priors, but also solves the non-smoothness problem caused by fast sampling.

[0017] 2. This invention solves the nonlinear problem in solving the inverse problem of speckle noise suppression optimization by analyzing the characteristics of speckle noise.

[0018] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by means of embodiments of the invention. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the non-smooth OCT denoising method that integrates efficient diffusion sampling priors proposed in this invention.

[0020] Figure 2 The diagram illustrates the comparison between linear and nonlinear inverse problems; the first row (linear) shows the restoration of images with missing pixels; the second row (linear) shows image denoising with additive noise removed; and the third row (nonlinear) shows speckle suppression with multiplicative speckle removal in real OCT images.

[0021] Figure 3 Manifold diagrams are generated for the concepts of various diffusion processes; where a represents the diffusion process of image generation; b represents the Manifold Constrained Gradients (MCG) method for linear inverse problems; c represents the DPS method for nonlinear inverse problems; and d represents the BOMO method for nonlinear inverse problems proposed in this invention.

[0022] Figure 4 This section provides a comparison between the feature maps and the statistical characteristic maps; where a is the noise feature map of Gaussian noise and speckle noise, and b is the statistical characteristic map of Gaussian noise distribution and speckle noise distribution.

[0023] Figure 5 This diagram illustrates the training and inference stages of the BOMO-accelerated speckle suppression method proposed in this invention, which integrates efficient diffusion sampling priors with non-smooth OCT denoising.

[0024] Figure 6 This invention provides a comparison of pseudo-color visualization of despeckled images and residual maps corresponding to real high-quality images.

[0025] Figure 7 This is a pseudo-color comparison result of the simulated speckle suppression of noisy GOALS images in this invention.

[0026] Figure 8 This is a pseudo-color comparison result of the simulated speckle suppression of noisy GOALS images in this invention.

[0027] Figure 9 This is a comparison chart showing the efficiency analysis of speckle suppression using various diffusion methods based on the CMOCT dataset in this invention. Detailed Implementation

[0028] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0029] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to provide some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0030] Please see Figure 1 and Figure 5 This invention proposes a non-smooth OCT denoising method that integrates efficient diffusion sampling priors, wherein... Figure 5 The overall framework of the present invention is illustrated, including a training phase and an inference phase. The method includes the following steps:

[0031] Step 1: Obtain degraded OCT observation images; characterize the degraded OCT observation images as Gamma distributions; construct a data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution.

[0032] In step 1, the degraded OCT observation image is characterized as a Gamma distribution, and the corresponding relationship in the process is as follows:

[0033] ;

[0034] in, Indicates the image without speckle. Degraded OCT observation images The distribution Indicates a speckle-free image of Power of 1 Indicates multiple views, Represents the Gamma function. Represents an exponential function;

[0035] It should be noted that you should refer to [link / reference]. Figure 4 Speckle noise differs significantly from Gaussian noise in both visual characteristics and statistical distribution. It is multiplicative noise and is usually modeled as a Gamma distribution.

[0036] In the step of constructing the data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution, the corresponding relationship in the process is as follows:

[0037] ;

[0038] in, Represents the logarithmic function. This represents random speckle noise. Indicates pixel index, This represents the observed image pixel value under the index value. This represents the pixel value of the sharp image at the index value. Represents a constant.

[0039] It should be noted that you should refer to [link / reference]. Figure 2 OCT speckle suppression belongs to the nonlinear inverse problem shown in the third row, which is fundamentally different from the linear inverse problems in the first two rows (such as pixel missing and Gaussian noise). Furthermore, this data fidelity term is essentially the negative log-likelihood function of the degraded image under the Gamma distribution assumption, used to constrain the degree of matching between the solution and the observed data during the optimization process.

[0040] Step 2: Use a pre-trained unconditional fractional diffusion model to construct a diffusion denoising prior through implicit reverse diffusion sampling.

[0041] In step 2, a pre-trained unconditional fractional diffusion model is used to construct a diffusion denoising prior through implicit inverse diffusion sampling. Specifically, this includes the following steps:

[0042] Obtain clean OCT images without speckle as training samples;

[0043] Based on the training samples, a time-conditional neural network is trained using the score matching method. By estimating the gradient of the perturbation data distribution under different noise levels, a pre-trained unconditional fractional diffusion model is obtained.

[0044] Set the total number of steps, step size, and noise scheduling parameters for each step of the reverse diffusion sampling;

[0045] Starting from random noise with a standard normal distribution, the pre-trained unconditional fractional diffusion model is used to perform an accelerated back diffusion process according to the noise scheduling parameters, and the denoised image is generated step by step.

[0046] The accelerated back-diffusion process is described as a denoising function that takes a noisy image as input and outputs a denoised image, which serves as a priori for diffusion denoising.

[0047] Starting from random noise with a standard normal distribution, and utilizing the pre-trained unconditional fractional diffusion model, an accelerated back diffusion process is executed according to the noise scheduling parameters. The corresponding relationship for this process is as follows:

[0048] ;

[0049] in, This represents the data sample of the next period in the diffusion inverse sampling. state, Indicates hyperparameters, This represents a pre-trained unconditional score diffusion model. This represents the currently estimated noise level. Indicates the diffusion process. Indicates the first The noise intensity of the step, This represents the random noise term.

[0050] It should be noted that implicit backward diffusion sampling is a step-by-step sampling method. It does not strictly follow the explicit probability flow of successive iterations, but instead directly performs state transitions through the aforementioned update rules, thereby significantly reducing the number of sampling steps and achieving acceleration. However, this step-by-step sampling update method introduces discontinuities or non-differentiable points into the constructed objective function, forming a "non-smooth" optimization problem. Therefore, subsequent steps of this invention employ the Bregman iterative algorithm, specifically designed for optimizing non-smooth functions, for solving the problem.

[0051] Step 3: Combine the data fidelity term of nonlinear speckle suppression with the diffusion denoising prior to construct a non-smooth function.

[0052] In step 3, the data fidelity term of nonlinear speckle suppression is combined with the diffusion denoising prior to construct a non-smooth function, specifically including:

[0053] Accept data fidelity terms for nonlinear speckle suppression and diffusion denoising priors;

[0054] Based on the restoration requirements of speckle suppression in OCT images, hyperparameters are set to balance the relative weights of data fidelity terms and diffusion denoising priors.

[0055] The data fidelity term of nonlinear speckle suppression, the diffusion denoising prior, and the hyperparameters of the relative weights are linearly combined to form a non-smooth function for the speckle-free image to be recovered.

[0056] The data fidelity term of nonlinear speckle suppression, the diffusion denoising prior, and the hyperparameters of the relative weights are linearly combined to form a non-smooth function about the speckle-free image to be recovered. The corresponding relationship in this process is as follows:

[0057] ;

[0058] in, The parameter represents the parameter that makes the function reach its minimum value. Hyperparameters representing relative weights This represents the denoiser prior derived using the diffusion model.

[0059] It should be noted that since the data fidelity term originates from the negative log-likelihood of the Gamma distribution, its form includes both logarithmic and fractional terms. When the estimated sharp image pixel value approaches zero during the iteration process, the gradient of this term tends towards infinity or becomes undefined, causing the objective function to be non-differentiable at that point, thus constituting a non-smooth optimization problem. Traditional gradient descent-based smooth optimization algorithms may fail or converge slowly on such problems. Therefore, this invention employs the Bregman iterative algorithm, suitable for non-smooth optimization. By introducing intermediate variables and the Bregman distance, it decomposes the original problem into solvable subproblems, thereby robustly and efficiently handling the non-smoothness introduced by implicit accelerated sampling and the data fidelity term.

[0060] For further details, please refer to Figure 3 ,exist Figure 3 Figure 'a' illustrates the process of using a traditional diffusion model for image generation, where the sampling path is outside the data manifold, resulting in low efficiency. Figure 3 In section b, the manifold-constrained gradient (MCG) method is shown for linear inverse problems, where the samples, although constrained, deviate from the true data distribution; Figure 3 In section c, diffuse posterior sampling (DPS) is shown for nonlinear inverse problems, but the samples tend to deviate from the generating manifold during measurement. In contrast, the BOMO method proposed in this invention (in...) Figure 3 The implicit sampling (d) accelerates the process, making the sampling process closer to the data manifold, and effectively prevents sample deviation during measurement updates, thereby significantly reducing computation time while ensuring reconstruction quality.

[0061] Step 4: Initialize the image estimates and intermediate variable values, and use the Bregman iterative algorithm to optimize the solution of the non-smooth function. By initializing the image estimates and the degraded OCT observation image, update the intermediate variable values ​​to obtain the updated intermediate variable values.

[0062] In step 4, the image estimates and intermediate variable values ​​are initialized, and the Bregman iterative algorithm is used to optimize the solution of the non-smooth function. By initializing the image estimates and the degraded OCT observation image, the intermediate variable values ​​are updated to obtain the updated intermediate variable values, specifically including:

[0063] Sampling is performed from a preset probability distribution to generate a noisy image of the same size as the degraded OCT observation image, which serves as the initial estimated image to be restored without speckle.

[0064] Assign zero initial values ​​to the intermediate variables associated with the data fidelity terms in the non-smooth function to obtain initialized intermediate variable values;

[0065] The initial estimated image without speckle to be recovered is set as the current image estimate of the first iteration, and the initialized intermediate variable values ​​are set as the current intermediate variable values ​​of the first iteration.

[0066] Based on the current image estimate and the degraded OCT observation image, the gradient of the data fidelity term in the non-smooth function is calculated, and the current intermediate variable value is updated to obtain the updated intermediate variable value.

[0067] Based on the current image estimate and the degraded OCT observation image, the gradient of the data fidelity term in the non-smooth function is calculated, and the current intermediate variable value is updated. The corresponding relationship in this process is as follows:

[0068] ;

[0069] in, Indicates the first In the next iteration, the speckle-free image is solved. The intermediate variable value introduced at that time, Indicates the image without speckle. Find the gradient. Indicates data fidelity.

[0070] Step 5: Using the updated intermediate variable values ​​as constraints, solve the denoising subproblem dominated by the diffusion denoising prior to obtain the updated image estimate.

[0071] In step 5, the updated intermediate variable values ​​are used as constraints to solve the diffusion-based denoising prior-dominated denoising subproblem. The corresponding relationship in the process is as follows:

[0072] ;

[0073] in, Indicates the first During the next iteration, the speckle-free image is processed. The current estimate, Indicates the mining of speckle-free images The regularization term of the prior information, Represents the Bregman distance. Represents the prior function for diffusion denoising. At point The subgradient at that point.

[0074] It should be noted that a non-smooth function refers to an objective function that contains non-differentiable or discontinuous terms. For example, the data fidelity term in this invention contains logarithmic and fractional terms, and is non-differentiable when some pixel values ​​are zero, which is a typical non-smooth optimization problem. To solve this type of problem, this invention uses the Bregman iterative algorithm, which is suitable for non-smooth function optimization and has good convergence and stability.

[0075] Step 6: Repeat steps 4 and 5 iteratively. When the number of iterations reaches the preset maximum number of iterations, and the difference between the image estimates obtained from two adjacent iterations is less than a preset threshold, output the image estimate obtained from the final iteration as the optimal solution of the non-smooth function to obtain the final speckle-free OCT image.

[0076] Experimental evaluation was conducted to verify the effectiveness of the present invention;

[0077] Implementation Details: All traditional speckle suppression algorithms, including ANLM, WKSVD, and WBM3D, were run in a MATLAB (R2013) environment on a PC equipped with an Intel(R) Core(TM) i7-7700 CPU @ 3.30GHz, and their speckle suppression performance was achieved through manual parameter tuning. The following diffusion-based methods were used in all experiments: DDPM, DDIM, ODDM, MCG, DiffPIR, DPS, SPIS, and the proposed BOMO framework. To ensure fair comparisons between different algorithms, all plug-and-play priors were derived from the same pre-trained diffusion model. All diffusion-based methods were run in a PyTorch environment using the Adam optimizer, with a unified hardware platform of an NVIDIA RTX 2080TI graphics card equipped with 48GB of VRAM. The image size of the training data was uniformly adjusted to 512×512 pixels, and the batch size for all experiments was 1.

[0078] Datasets: Extensive experiments were conducted on two real OCT datasets (ASOCT and CMOCT) and one simulated original OCT dataset (GOALS) to evaluate the performance of various methods. The private datasets ASOCT and CMOCT were acquired using the CASIA2 device (Tomey Corporation, Japan), while the public dataset GOALS was acquired from the SDOCT imaging system (Bioptigen Corporation, USA).

[0079] Specifically, the AS-OCT dataset contains 430 high-quality-noise paired images of size 2131×1600, of which 390 high-quality images were used for training and the remaining 40 high-quality-noise paired images were used for testing. The CM-OCT dataset contains 200 high-quality-noise paired images of size 1065×1465, providing large-field-of-view images of ciliary muscle structures; 160 high-quality images in this dataset were used for training, and the remaining paired images were reserved for testing. The GOALS dataset contains only 180 high-quality images of 900×450 pixels, each image accompanied by multi-layer segmentation labels including the retinal nerve fiber layer, ganglion cell-internal plexiform layer, and choroid layer. Speckle noise at three noise levels (ε2=1 / L=0.01, 0.02, 0.04) was simulated on the GOALS dataset.

[0080] Baseline Methods: BOMO's performance was compared against several competing methods. This comparative analysis covered three different methodologies: (1) traditional model-based methods, including WBM3D, ANLM, and WKSVD, which rely on existing mathematical priors for speckle suppression; (2) leading diffusion solvers for general linear inverse problems, particularly DiffPIR and MCG; and (3) contemporary diffusion solvers for nonlinear inverse problems, namely DPS, ODDM, and SPIS. Among them, ODDM and SPIS are specifically designed for speckle suppression in OCT images.

[0081] Evaluation metrics: Four metrics were used for evaluation: Peak Signal-to-Noise Ratio (PSNR) and Mean Squared Error (MSE) for pixel-level fidelity; and Structural Similarity Index (SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) for perceptual similarity. Notably, LPIPS, trained based on human judgment, effectively measures high-level feature differences. Better performance is characterized by higher PSNR / SSIM values ​​and lower MSE / LPIPS values. Furthermore, to assess the impact of speckle suppression on clinical analysis, this experiment calculated F1 scores and Intersection over Union (IoU) on simulated images to evaluate retinal layer segmentation effectiveness.

[0082] The speckle suppression performance was compared and evaluated on real degraded OCT images from the ASOCT and CMOCT datasets. Quantitative results are summarized in Table I, showing that the proposed BOMO framework achieves state-of-the-art performance on almost all evaluation metrics. Specifically, BOMO achieves higher PSNR and SSIM values ​​while maintaining lower MSE and LPIPS scores. A notable exception is the WKSVD method, which achieves the lowest (best) LPIPS value on the CMOCT dataset. However, this single performance advantage is offset by WKSVD's significantly poorer results on PSNR, SSIM, and MSE metrics, indicating that its perceptual gain is not correlated with overall fidelity.

[0083] Table I: Performance Comparison on Real-World Degraded ASOCT and CMOCT Datasets

[0084]

[0085] In addition, please see Figure 6 ,exist Figure 6 The paper provides a pseudo-color visualization comparison of despec images and displays the residual maps corresponding to real high-quality images. Key observations reveal that recent works like SPIS and traditional algorithms still retain significant speckle noise in structurally complex regions and relatively uniform backgrounds, indicating insufficient suppression. In contrast, other diffusion-based solvers demonstrate superior suppression performance in background regions. The proposed BOMO method, however, excels in structural fidelity, particularly in preserving the anterior capsule and iris boundaries in the green and cyan regions (marked with red arrows), respectively.

[0086] To further explore the generalization ability and potential advantages of BOMO in clinical applications, this experiment conducted synthetic speckle suppression experiments on the high-quality GOALS dataset at different noise levels, followed by multi-task segmentation analysis. Specifically, we first used different contrast methods to despeczema on the synthesized GOALS dataset at three specific noise levels, and then used the processed images as input to the subsequent multi-task segmentation model to identify the retinal nerve fiber layer, ganglion cell-internal plexiform complex, and choroidal layer.

[0087] The quantitative results in Table II demonstrate that BOMO exhibits superior performance in both speckle suppression and downstream segmentation tasks. Notably, this advantage is maintained across all tested noise levels, with BOMO consistently achieving the best performance metrics. Furthermore, its performance demonstrates remarkable robustness: with increasing noise levels, performance decreases only slightly, further highlighting its reliability for clinical applications under various image quality conditions.

[0088] Table II: Comparison of speckle suppression and downstream segmentation performance of different methods on the GOALS dataset

[0089]

[0090]

[0091]

[0092] In addition, please see Figure 7 ,exist Figure 7 A visual evaluation of speckle suppression performance is provided at a noise level ε²=0.01, showing a pseudo-color image and its corresponding residual map. Please refer to [link / reference]. Figure 8 ,exist Figure 8 In the segmentation results, these visual results perfectly match the quantitative analysis. Observation of the residual plot reveals that methods such as WBM3D, ANLM, WKSVD, and DiffPIR retain a large amount of structural information in the residuals, indicating the presence of undesirable residues. This over-smoothing phenomenon directly affects the performance of downstream tasks, causing their segmentation results to fail to accurately delineate the target layer boundaries. In contrast, SPIS, MCG, DPS, and the proposed BOMO method produced satisfactory segmentation results, which, except for a small error at the end of the choroid layer, highly agree with the real labels. A key observation is that all methods contribute to improving segmentation performance compared to the noisy baseline; however, it is the proposed BOMO method that achieves the highest IoU value, confirming its superior overall performance.

[0093] To quantitatively evaluate the contribution of each strategy in the BOMO framework, this invention also conducted ablation experiments, applying standard DDPM without any speckle suppression strategy as a baseline on real-world CMOCT images. Subsequently, this invention gradually introduced various core innovations to isolate their effects: (1) Data fidelity term for nonlinear inverse speckle suppression (labeled "Nonlinear"): The standard sampling process is replaced with a method specifically designed for nonlinear inverse problems. The posterior regularization term (labeled "Ours") specifically designed in this invention was compared with the established data fidelity term used in DPS. (2) Implicit sampling for acceleration within the Bregman iteration framework, labeled "SU": To address the computational burden of the diffusion model, this invention implements an implicit sampling process that utilizes Bregman iteration for non-smooth optimization. The symbols "-s" and "+s" represent the removal and addition of this acceleration strategy, respectively.

[0094] The quantitative results in Table III clearly demonstrate the effectiveness of each strategy in achieving satisfactory speckle suppression. The introduction of a new data fidelity term confirms its crucial role in performance improvements related to modeling accuracy. Furthermore, the acceleration strategy exhibits high computational efficiency.

[0095] Table III: Ablation experiments of the proposed optimized method on the CMOCT dataset

[0096]

[0097] To evaluate the effectiveness of the Bregman iteration in addressing the inherent non-smooth optimization problem of the implicit sampling process of this invention, comparative experiments were conducted at a range of sampling steps (from 1000 to 50, decreasing at equal intervals). Please refer to [link to relevant documentation]. Figure 9 ,exist Figure 9 The visualized quantitative results revealed significant differences in robustness. Competitor methods (i.e., DPS and MCG) showed a significant performance decline as the number of sampling steps decreased.

[0098] In terms of computation time, DPS, MCG, and the proposed BOMO exhibited nearly identical time cost curves. Although DiffPIR took less time with the same number of steps, its reconstruction quality consistently lagged behind BOMO at each sampling point of the same duration. This is attributed to BOMO's accurate data fidelity term and its Bregman iteration's robust handling of non-smooth optimization problems, highlighting its superior efficiency and making it well-suited for clinical deployment. Notably, to maintain fairness in the experiment, the results for DPS, MCG, and DiffPIR were obtained with 1000 samplings, while BOMO was evaluated using only 100 steps, further emphasizing its efficiency.

[0099] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0100] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0101] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A non-smooth OCT denoising method incorporating efficient diffusion sampling prior, characterized in that, The method includes the following steps: Step 1: Acquire degraded OCT observation images; characterize the degraded OCT observation images as a Gamma distribution; construct a data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution; Step 2: Using a pre-trained unconditional fractional diffusion model, a diffusion denoising prior is constructed through implicit reverse diffusion sampling; Step 3: Combine the data fidelity term of nonlinear speckle suppression with the diffusion denoising prior to construct a non-smooth function; Step 4: Initialize the image estimates and intermediate variable values, and use the Bregman iterative algorithm to optimize the solution of the non-smooth function. By initializing the image estimates and the degraded OCT observation image, update the intermediate variable values ​​to obtain the updated intermediate variable values. Step 5: Using the updated intermediate variable values ​​as constraints, solve the denoising subproblem dominated by the diffusion denoising prior to obtain the updated image estimate. Step 6: Repeat steps 4 and 5 in an iterative manner. When the number of iterations reaches the preset maximum number of iterations, and the difference between the image estimates obtained from two adjacent iterations is less than a preset threshold, output the image estimate obtained from the final iteration as the optimal solution of the non-smooth function to obtain the final speckle-free OCT image. In step 2, a pre-trained unconditional fractional diffusion model is used to construct a diffusion denoising prior through implicit inverse diffusion sampling. Specifically, this includes the following steps: Obtain clean OCT images without speckle as training samples; Based on the training samples, a time-conditional neural network is trained using the score matching method. By estimating the gradient of the perturbation data distribution under different noise levels, a pre-trained unconditional fractional diffusion model is obtained. Set the total number of steps, step size, and noise scheduling parameters for each step of the reverse diffusion sampling; Starting from random noise with a standard normal distribution, the pre-trained unconditional fractional diffusion model is used to perform an accelerated back diffusion process according to the noise scheduling parameters, and the denoised image is generated step by step. The accelerated back-diffusion process is described as receiving a noisy image as input and outputting a denoised image as output, which serves as a priori for diffusion denoising. Starting from random noise with a standard normal distribution, the pre-trained unconditional fractional diffusion model is used to execute an accelerated back diffusion process according to noise scheduling parameters. The corresponding relationship for this process is as follows: ； in, This represents the data sample of the next period in the diffusion inverse sampling. state, Indicates hyperparameters, This represents a pre-trained unconditional score diffusion model. This represents the currently estimated noise level. Indicates the diffusion process. Indicates the first The noise intensity of the step, Represents random noise; In step 4, the image estimate and intermediate variable values ​​are initialized, and the Bregman iterative algorithm is used to optimize the solution of the non-smooth function. By initializing the image estimate and the degraded OCT observation image, the intermediate variable values ​​are updated to obtain the updated intermediate variable values. Specifically, this includes: Sampling is performed from a preset probability distribution to generate a noisy image of the same size as the degraded OCT observation image, which serves as the initial estimated image to be restored without speckle. Assign zero initial values ​​to the intermediate variables associated with the data fidelity terms in the non-smooth function to obtain initialized intermediate variable values; The initial estimated image without speckle to be recovered is set as the current image estimate of the first iteration, and the initialized intermediate variable values ​​are set as the current intermediate variable values ​​of the first iteration. Based on the current image estimate and the degraded OCT observation image, the gradient of the data fidelity term in the non-smooth function is calculated, and the current intermediate variable value is updated to obtain the updated intermediate variable value.

2. The non-smooth OCT denoising method according to claim 1, characterized in that, In step 1, the degraded OCT observation image is characterized as a Gamma distribution, and the corresponding relationship in the process is as follows: ； in, Indicates the image without speckle. Degraded OCT observation images The distribution Indicates a speckle-free image of Power of 1 Indicates multiple views, Represents the Gamma function. Represents an exponential function; In the step of constructing the data fidelity term for nonlinear speckle suppression based on the distribution characteristics of the Gamma distribution, the corresponding relationship in the process is as follows: ； in, Represents the logarithmic function. This represents random speckle noise. Indicates pixel index, This represents the observed image pixel value under the index value. This represents the pixel value of the sharp image at the index value. Represents a constant.

3. The non-smooth OCT denoising method according to claim 2, characterized in that, In step 3, the data fidelity term of nonlinear speckle suppression is combined with the diffusion denoising prior to construct a non-smooth function, specifically including: Accept data fidelity terms for nonlinear speckle suppression and diffusion denoising priors; Based on the restoration requirements of speckle suppression in OCT images, hyperparameters are set to balance the relative weights of data fidelity terms and diffusion denoising priors. The data fidelity term of nonlinear speckle suppression, the diffusion denoising prior, and the hyperparameters of the relative weights are linearly combined to form a non-smooth function for the speckle-free image to be recovered.

4. The non-smooth OCT denoising method according to claim 3, characterized in that, The data fidelity term of nonlinear speckle suppression, the diffusion denoising prior, and the hyperparameters of the relative weights are linearly combined to form a non-smooth function about the speckle-free image to be recovered. The corresponding relationship in this process is as follows: ； in, The parameter represents the parameter that makes the function reach its minimum value. Hyperparameters representing relative weights This represents the denoiser prior derived using the diffusion model.

5. The non-smooth OCT denoising method according to claim 4, characterized in that, Based on the current image estimate and the degraded OCT observation image, the gradient of the data fidelity term in the non-smooth function is calculated, and the current intermediate variable value is updated. The corresponding relationship in this process is as follows: ； in, Indicates the first In the next iteration, the speckle-free image is solved. The intermediate variable value introduced at that time, Indicates the image without speckle. Find the gradient. This indicates a data fidelity item.

6. The non-smooth OCT denoising method according to claim 5, characterized in that, In step 5, the updated intermediate variable values ​​are used as constraints to solve the diffusion-based denoising prior-dominated denoising subproblem. The corresponding relationship in the process is as follows: ； in, Indicates the first During the next iteration, the speckle-free image is processed. The current estimate, Indicates the mining of speckle-free images The regularization term of the prior information, Represents the Bregman distance. Represents the prior function for diffusion denoising. At point The subgradient at that point.

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