Self-adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism

Abstract

The invention discloses a self-adaptive image denoising method based on a dynamic fractional order and memristor introspection mechanism, and relates to the field of image denoising, and the method comprises the steps: inputting a noisy image, and constructing a dynamic fractional order guidance matrix of the image; constructing a dynamic fractional order total variation regularization model based on the dynamic fractional order order guidance matrix; solving the dynamic fractional order total variation regularization model by adopting an optimization algorithm based on a dual-mode memristor introspection mechanism; judging whether the iteration process meets a preset convergence condition or not, and if yes, outputting a final de-noised image; according to the method, a high-fidelity denoising effect is realized by constructing a complete self-adaptive closed loop from an image local structure to a differential operator behavior and then to an optimization process strategy.

Description

An Adaptive Image Denoising Method Based on Dynamic Fractional Order and Memristor Introspection Mechanism Technical Field

[0001] This invention belongs to the field of image denoising, and in particular relates to an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism. Background Technology

[0002] Image denoising is a fundamental and crucial problem in computer vision and image processing. Its goal is to recover the cleanest possible original image from a noisy image, a prerequisite for subsequent advanced vision tasks (such as object detection, image segmentation, and medical image analysis). Classical image denoising methods, such as Gaussian filtering and median filtering, while simple to implement, often lead to severe blurring of high-frequency details like image edges and textures due to their "one-size-fits-all" approach. To address this issue, models based on partial differential equations (PDEs), especially total variation (TV) models, have become a research hotspot due to their superior edge-preserving properties.

[0003] Total variational models are more accurate than traditional linear filtering in preserving image structure, but their inherent integer-order differential operators (usually first-order) have limitations in describing local image features. Integer-order operators cannot differentiate between smooth regions and complex texture regions, limiting further improvements in denoising performance. Extending integer-order models to fractional-order models is becoming a research trend in image processing. Fractional-order calculus, due to its "memory" and "non-locality" properties, can provide richer detail description capabilities between integer-order and fractional-order calculus, theoretically better characterizing image texture information. However, most existing fractional-order denoising methods use a fixed, globally uniform fractional order, ignoring the spatial non-uniformity of image content. Different regions (such as smooth areas and edge regions) require different optimal processing methods, resulting in fixed-order methods still failing to perfectly balance denoising and detail preservation.

[0004] Furthermore, iterative algorithms, such as the Alternating Directional Multiplier Method (ADMM), are typically used to solve these PDE-based optimization models. The convergence performance of these algorithms, such as convergence speed and the quality of the final solution, heavily depends on the setting of key parameters (e.g., regularization parameters and penalty parameters). Controlling and optimizing the performance of the algorithm's iterative process has always been a research focus. Currently, most of these parameters are based on empirical values ​​or fixed tuning strategies, lacking a dynamic response mechanism for the iterative process itself. This "blind" iterative approach is like exploring a complex energy function surface without feedback, easily getting trapped in local optima, leading to incomplete denoising or artifacts, and also affecting the algorithm's convergence efficiency.

[0005] Memristors, as nonlinear two-terminal devices with memory capabilities, can dynamically adjust their resistance based on the history of the charge flowing through them. This unique "introspection" and "memory" characteristic offers possibilities for designing novel adaptive optimization algorithms. Current research on their dynamic characteristics is mostly limited to circuit simulation and neural network hardware implementation. Abstracting the dynamic introspection mechanism of memristors into a mathematical model and using it to guide and control the iterative process of complex optimization algorithms, especially in fractional-order image processing models, has been rarely reported. How to leverage the introspection mechanism of memristors to design an intelligent optimization strategy capable of sensing the iterative state and adaptively adjusting key parameters in real time is a highly innovative potential direction for improving the efficiency and effectiveness of denoising model solving. Summary of the Invention

[0006] The purpose of this invention is to address the technical problem of poor image denoising performance in existing technologies by proposing an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0007] This invention is achieved through the following technical solution: an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism, comprising the following steps: S1, inputting a noisy image and constructing a dynamic fractional order guidance matrix for the image; specifically, calculating the local structural complexity of each pixel in the image based on multi-scale structural entropy, and labeling the complexity as a fractional order unique to that pixel through a nonlinear mapping function, generating a dynamic fractional order guidance matrix V with the same size as the noisy image; S2, constructing a dynamic fractional total variational regularization model based on the dynamic fractional order guidance matrix V; specifically, decomposing the variable order fractional differential operation into multiple fixed basis kernels. The standard convolution of the image and a pixel-level weighted summation of a dynamic weight mask generated by the order guidance matrix V are used to construct an energy functional containing a data fidelity term and a dynamic fractional total variation regularization term; S3, the dynamic fractional total variation regularization model is solved using an optimization algorithm based on a dual-mode memristor introspection mechanism; specifically, a dual-mode memristor mathematical model containing short-term and long-term memristor values ​​is constructed to perceive the immediate effect and long-term trend of the iteration process, and the key parameters of the optimization algorithm are dynamically adjusted accordingly to perform iterative solution and obtain the denoised image; S4, it is determined whether the iteration process meets the preset convergence condition. If it does, the final denoised image is output.

[0008] A storage device that stores instructions and data for implementing an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0009] An adaptive image denoising device based on dynamic fractional order and memristor introspection mechanism includes: a processor and a storage device; the processor loads and executes instructions and data in the storage device to implement an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0010] This invention has the following beneficial effects: It establishes a dynamic fractional order calibration mechanism based on multi-scale structural entropy (MSE). Compared with single-scale information entropy, multi-scale structural entropy can more robustly and accurately capture the true complexity of the local environment of a pixel, thereby providing more refined guidance for subsequent differentiation operations. Finally, by constructing a complete adaptive closed loop from local image structure to differential operator behavior and then to optimization process strategy, high-fidelity denoising effect is achieved. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 is a schematic diagram of the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism of the present invention; Figure 2 is a schematic diagram of Gaussian pyramid construction; Figure 3 is a schematic diagram of dual-mode memristor model structure; Figure 4 is a schematic diagram of ADMM iterative solution process; Figure 5 is the original image of "lena.png" in the dataset before denoising; Figure 6 is the denoised image after the implementation of the method of this scheme; Figure 7 is a schematic diagram of the hardware device of the present invention. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Example 1: Referring to Figure 1, this invention is an adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism, including the following steps: S1, input a noisy image and construct a dynamic fractional order guidance matrix for the image; specifically: calculate the local structural complexity of each pixel in the image based on multi-scale structural entropy, and label the complexity as a unique fractional order of the pixel through a nonlinear mapping function, generating a dynamic fractional order guidance matrix V with the same size as the noisy image; it should be noted that the construction of the dynamic fractional order guidance matrix in step S1 specifically includes: S11, constructing an L-layer Gaussian pyramid for the input noisy image; S12, calculating the local information entropy of each pixel in each layer of the pyramid; S13, upsampling the local information entropy maps of each layer to the original image size, and performing weighted fusion to generate a multi-scale structural entropy map HMSE(x,y); S14, through a nonlinear mapping function:

[0015] The multi-scale structural entropy map HMSE(x,y) is mapped to the fractional order of each pixel, where vmax is the maximum order, HT is the entropy threshold adaptive by Otsu's method, α is the slope control parameter, and β is the offset correction parameter.

[0016] As one embodiment, in order to overcome the sensitivity of a single neighborhood window to noise and scale changes, the input noisy image is first processed.

[0017] Perform multi-scale spatial decomposition. Specifically, construct a... The structure of the Gaussian pyramid is shown in Figure 2.

[0018] Let the 0th layer be... . No. Layer Image (in ) by the first Layer Image First, Gaussian blur is applied, then downsampling is performed. In this scheme, the standard deviation of the Gaussian kernel is... The value is set to 1.5, the downsampling factor is 2, and the number of pyramid levels is [not specified]. The value is determined to be 3.

[0019] Next is the calculation and fusion of local structural entropy. This is done at each level of the pyramid. Above, for each pixel Take one Local neighborhood window ,in The value is determined to be 5, and its local information entropy is calculated. :

[0020] in grayscale In the window The probability of occurrence in the matrix. This yields the information entropy response of each pixel at different scales:

[0021] Next, multi-scale structural entropy is generated.

[0022] To integrate multi-scale information to generate a unified and robust structure metric, this scheme defines multi-scale structure entropy. .

[0023] First, the entropy diagrams of each bottom layer of the pyramid are created. The image is restored to the same size as the original image by upsampling, denoted as... Then, through weighted fusion, we obtain... :

[0024] Weight The design reflects an emphasis on information at different scales, giving higher weight to more refined, high-resolution scales. The weights are determined as follows: .for The settings, specifically the weights are as follows: Thus generated It can more effectively suppress the interference of noise on entropy calculation and more accurately reflect the true width of the edge and the actual range of the texture.

[0025] Finally, the dynamic fractional order is completed. Nonlinear mapping calibration. Based on more reliable multi-scale structural entropy. To achieve a more accurate order assignment, a nonlinear mapping function is established from this entropy value to fractional orders.

[0026] Each parameter was determined to ensure the reproducibility of the solution: This is the final output of this step, i.e., the pixels. The dynamic fractional order at the point; It is the maximum theoretical value of the fractional order, determined to be 2.0; It is the slope control parameter of the mapping function, which is set to 3.0; It is an adaptive entropy threshold that distinguishes between smooth and non-smooth regions. Its value is obtained by applying the multi-scale structural entropy matrix of the entire image. The threshold decision is calculated using the Otsu method (OTSU), which makes the threshold decision more robust than the decision based on single-scale entropy. This is the zero-point offset correction parameter, whose value is determined by the function when the independent variable is zero. ,make sure Approaching zero time It also strictly approaches zero.

[0027] This step yields a highly refined dynamic fractional-order guidance matrix that is identical in size to the image. This matrix will directly guide the specific behavior of the differential operator in the next step.

[0028] S2. Based on the dynamic fractional-order guidance matrix V, construct a dynamic fractional-order total variation regularization model; specifically, decompose the variable-order fractional-order differential operation into a standard convolution of multiple fixed base kernels with the image, and a pixel-level weighted summation of a dynamic weight mask generated by the guidance matrix V, and construct an energy functional containing a data fidelity term and a dynamic fractional-order total variation regularization term; it should be noted that the specific implementation of step S2 is as follows: The fractional differential of order 1 is expressed as: Where Bj is a fixed set of basis difference kernels, J is the number of basis kernels, and Wj(v) is a dynamic weight mask that depends on the order v, implemented through a pre-computed interpolation polynomial. ⊙ represents the convolution operation, and ⊙ represents the Hadamard product.

[0029] Energy functional for constructing a denoising model The goal is to find the image that minimizes the functional. :

[0030] in The denoised image is the solution to be found. The image contains noise; the first term on the right side of the equation is the data fidelity term. The first term is the regularization parameter; the second term is the dynamic fractional total variation regularization term. It is an L1 norm. It represents the Hadamardi (or Hadama) stack.

[0031] It should be noted that the basis difference kernel includes a 0th-order identity operator, a 1st-order difference operator, and a 2nd-order Laplace operator, and the dynamic weight mask Wj(v) is a predefined polynomial function of order v.

[0032] As one example, this step follows the order guidance matrix generated in the previous step. We construct a novel Dynamic Fractional Total Variation (DFOTV) model. To address the inefficiency of pixel-by-pixel fractional differentiation operations, this approach formalizes the operation as a convolution operation between a fixed set of basis difference kernels and a dynamic mask. This significantly improves computational efficiency and makes the model easier to implement in parallel on modern computing architectures such as GPUs.

[0033] First, the basis kernel decomposition and dynamic masking of fractional derivatives are addressed. This invention employs the Grünwald-Letnikov (GL) definition to implement discrete fractional derivatives. This avoids direct pixel-by-pixel calculations that depend on the order. GL coefficients The huge computational overhead it brings, this solution will The difference of the order is approximated by a set of fixed basic nuclei. With a dynamically generated weight mask The combination of . Specifically, by expanding and simplifying the GL coefficients using Taylor series near integer order, we can obtain the following approximation:

[0034] In this plan, it is determined that , base core These correspond to discrete operators of order 0 (identity), order 1 (first-order difference), and order 2 (second-order Laplace), respectively. Dynamic weight mask. It's about order. The pre-calculated interpolation polynomial, for example: .

[0035] This method decomposes complex variable-order differential operations into three regular convolutions and one convolution based on the order guidance matrix. The pixel-level weighted summation significantly reduces computational complexity.

[0036] Next, the DFOTV energy functional is constructed. Based on the above efficient computational method, the energy functional of the denoising model is constructed. The goal is to find the image that minimizes the functional. :

[0037] in The denoised image is the solution to be found. The image contains noise; the first item is the data fidelity item. The first term is the regularization parameter, whose value will be dynamically adjusted in step three; the second term is the dynamic fractional total variation regularization term. It is an L1 norm. This represents the element-wise product. This model uses the order-guided matrix... Introducing a regularization term as a core variable establishes a direct link between image content and regularization strength.

[0038] S3. An optimization algorithm based on the dual-mode memristor introspection mechanism is used to solve the dynamic fractional-order total variational regularization model. Specifically, a dual-mode memristor mathematical model containing short-term and long-term memristor values ​​is constructed to perceive the immediate effect and long-term trend of the iterative process. Based on this, the key parameters of the optimization algorithm are dynamically adjusted, and iterative solutions are performed to obtain the denoised image. It should be noted that the construction of the dual-mode memristor mathematical model in step S3 specifically includes: S31. Based on the residual change of a single iteration... Update short-term memristor value Its update rules are as follows: Where σ(·) is the Sigmoid function, This is the short-term sensitivity coefficient; These are the preset maximum and minimum values ​​of the memristor, respectively; S32, update the long-term memristor value based on the stagnation indicator S(t) defined by the number of times the residual change is positive in the past Tw iterations. Its update rules are as follows:

[0039] Where η is the long-term memory accumulation rate.

[0040] It should be noted that the key parameters of the dynamic adjustment optimization algorithm in step S3 are as follows: the optimization algorithm is the alternating direction multiplier method, and its key parameters include the regularization parameter λ and the penalty parameter ρ; the update of the regularization parameter λ is dominated by the short-term memristor value, and the rule is as follows: The update of the penalty parameter ρ is jointly determined by the short-term memristor value and the long-term memristor value, according to the following rule: ;in, and Here, k is the basic parameter, and k is the long-term inhibition coefficient.

[0041] As one example, this step involves solving the DFOTV model in step S2, and an intelligent optimization algorithm inspired by the physical behavior of a dual-mode memristor is designed. This algorithm can not only adjust global parameters, but also introspectively perceive the "trend" and "quality" of the iteration, adaptively switching between "fast-forward" convergence and "cautious" exploration modes, thereby achieving faster convergence speed and the ability to escape local optima.

[0042] First, we construct a two-mode memristor model containing two internal state variables: short-term memristor value. and long-term memristor Its structure is shown in Figure 3.

[0043] in The immediate effect of responding to a single-step iteration, and the change in single-step residuals. Related:

[0044] in , The sigmoid function is the short-term sensitivity coefficient. . This is used to perceive the long-term trend of the iterative process. For this purpose, a "stagnation indicator" is defined. It counts the past (window length) During iteration The number of times the sign is positive. The update rules are as follows:

[0045] Among them, the rate of long-term memory accumulation When recent iterations do more harm than good, It will increase if it increases, and decrease if it decreases, thus reflecting the overall health of the iteration.

[0046] Secondly, utilize and For the regularization parameter in the ADMM algorithm and penalty parameters Perform collaborative, multi-modal adaptive updates. Regularization parameters. Updates are driven by short-term memristor values ​​to enable fast response:

[0047] Among them, the basic regularization parameters Penalty parameters The update is determined by the dual-mode memristor state to achieve the switching between "fast forward" and "cautious" modes:

[0048] Among them, the basic penalty parameters Long-term inhibition coefficient .

[0049] Finally, the ADMM iterative solution process is shown in Figure 4. Specifically, before each iteration, based on the dual-mode memristor introspection mechanism, the parameters required for the current iteration are first updated. and Subsequently, the alternating direction multiplier method (ADMM) was employed, by introducing auxiliary variables. and Lagrange multipliers In the In this iteration, the update operations are performed alternately in the following order: Update Image I: Fix Seeking answers regarding This is a quadratic programming subproblem. This problem can be solved efficiently in the frequency domain using the Fast Fourier Transform (FFT), and its update formula is:

[0050] in This represents the dynamic fractional gradient operator.

[0051] Update auxiliary variable Z: Fixed and Seeking answers regarding The L1 norm near-end problem. This problem has a closed-ended solution, which can be solved by the soft-thresholding operator. accomplish:

[0052] Update Lagrange multiplier U: Fixed and Perform dual variable updates:

[0053] These three update operations are executed cyclically until the convergence condition set in step S4 is met.

[0054] S4. Determine whether the iteration process meets the preset convergence condition. If it does, output the final denoised image.

[0055] As one embodiment, the present invention sets a dual iteration termination condition.

[0056] One is to reach the preset maximum number of iterations. In this plan, it is determined to be .

[0057] Secondly, the relative change between two adjacent iterations is less than a very small threshold. ,Right now:

[0058] in The iteration terminates when any of the conditions is met. The image generated in the last iteration is then displayed. As the final high-fidelity denoised image Output the results.

[0059] Example 2: To verify the effectiveness and advancement of the method proposed in this application, a series of simulation experiments were conducted, and a detailed performance comparison was performed with existing mainstream and cutting-edge image denoising methods. The experimental results fully demonstrate the significant advantages of this scheme in denoising performance, detail preservation capability, and computational efficiency.

[0060] The validation experiments for this scheme use two internationally recognized standard test image sets. The Set12 dataset contains 12 commonly used grayscale test images, mainly used to evaluate the algorithm's ability to process general image structures. The BSD68 dataset contains 68 natural images with richer content and more complex textures, which can better test the algorithm's ability to preserve details in complex scenes. In the experiments, Gaussian white noise of different intensities was added to all test images, with a noise standard deviation of [missing information]. The noise levels are set to 15 (low noise), 25 (medium noise), and 50 (high noise) respectively.

[0061] We employ two of the most authoritative image quality assessment metrics.

[0062] Peak Signal-to-Noise Ratio (PSNR): This mainly measures the similarity in pixel values ​​between the denoised image and the original noise-free image. The higher the PSNR, the better the noise suppression.

[0063] Structural Similarity (SSIM): This measure of image similarity in terms of brightness, contrast, and structure, and better reflects human visual perception. The higher the SSIM, the more intact the image's structure and texture are.

[0064] To comprehensively evaluate the performance of this scheme, two representative comparison methods were established: Comparison Method 1 (classical nonlocal method) adopts BM3D (Block-matching and 3D filtering), a landmark algorithm in the field of image denoising. This method searches for similar blocks in the image and performs collaborative filtering, and is recognized as a performance benchmark among non-deep learning methods.

[0065] Comparison Method 2 (Deep Learning Method) employs a classic deep learning denoising network, DnCNN (Denoising Convolutional Neural Network). This method trains a deep convolutional network on a large amount of data to learn the mapping from noisy images to noise residuals, representing the mainstream technology of current data-driven methods.

[0066] Denoising Performance Quantitative Comparison and Result Analysis: On the Set12 and BSD68 datasets, the average PSNR (unit: dB) and SSIM of our proposed method were statistically analyzed against those of the two comparative methods for different noise levels. The specific results are shown in Tables 1 and 2 below: Table 1: Comparison of Average PSNR / SSIM on the Set12 Dataset

[0067] Table 2: Comparison of mean PSNR / SSIM on the BSD68 dataset

[0068] Leading Overall Performance: As clearly seen from the two tables, regardless of the dataset or noise level, our proposed method achieves optimal results in both PSNR and SSIM, the two key metrics. This indicates that our method has reached an industry-leading level in both noise suppression and structure preservation. Figure 5 shows the original image of "lena.png" in the dataset before denoising, and Figure 6 shows the denoised image after implementing our proposed method.

[0069] Superior handling of complex textures: On the more complex BSD68 dataset, the advantages of this approach over the comparison methods are more pronounced (e.g., in...). At that time, SSIM outperformed BM3D by 0.018. This is thanks to the core innovation of this solution—the dynamic fractional differential operator. This operator can accurately match the optimal differential order for each pixel in the image, powerfully denoising in smooth areas and finely preserving details in textured areas, avoiding the blurring or smearing phenomena that may occur when methods such as BM3D process complex textures.

[0070] The potential of model-driven approaches: Notably, this approach, as a model-driven method that does not require massive training data, comprehensively outperforms the classic deep learning method DnCNN. This demonstrates that by constructing more sophisticated mathematical models (dynamic fractional order) and more intelligent optimization algorithms (memristor introspection mechanism), traditional model-driven frameworks still possess enormous innovative potential and performance advantages, without relying on expensive training processes.

[0071] Another major innovation of this scheme lies in the intelligent optimization solution based on the memristor introspection mechanism. To verify its efficiency, this scheme was compared with the traditional fixed-parameter ADMM algorithm in terms of the number of iterations required to achieve the same PSNR target value. The results are shown in Table 3: Table 3 Comparison of Iteration Count

[0072] The memristor introspection mechanism in this scheme can sense the "health" of the iteration process in real time, intelligently adjust the optimization parameters, "fast forward" when the iteration is going smoothly, and "cautiously explore" when it may get stuck in a local optimum. Therefore, as shown in the table above, this scheme can achieve the same excellent denoising effect with significantly fewer iterations, and the computational efficiency is improved by more than 40% compared with traditional fixed-parameter optimization algorithms. This greatly enhances the feasibility of this method in practical applications.

[0073] Example 3. Please refer to Figure 7. Figure 7 is a schematic diagram of the hardware device operation of an embodiment of the present invention. The hardware device specifically includes: an adaptive image denoising device 401 based on dynamic fractional order and memristor introspection mechanism, a processor 402, and a storage device 403.

[0074] An adaptive image denoising device 401 based on dynamic fractional order and memristor introspection mechanism: The adaptive image denoising device 401 based on dynamic fractional order and memristor introspection mechanism implements the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0075] Processor 402: The processor 402 loads and executes the instructions and data in the storage device 403 to implement the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0076] Storage device 403: The storage device 403 stores instructions and data; the storage device 403 is used to implement the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism.

[0077] Finally, the key to implementing the present invention lies in the construction of a pixel-level dynamic fractional differential operator based on the traditional total variation model, the core of which is the order. The generation mechanism abandons the globally fixed order and instead constructs a multi-scale Gaussian pyramid of the image and integrates local information entropy at each scale to generate a "multi-scale structural entropy (MSE)" that can more robustly and accurately reflect the local structural complexity of the image. Finally, through a nonlinear mapping function, this structural metric is calibrated to the unique and optimal fractional derivative order of each pixel.

[0078] To efficiently perform pixel-wise variable-order differential operations, a computational method based on kernel decomposition and dynamic mask convolution is proposed. This method innovatively decomposes the complex and computationally intensive variable-order fractional-order differential operation into a conventional convolution of the image with a few fixed kernels (such as 0th, 1st, and 2nd order difference operators), and a dynamic order guidance matrix. The generated weighted masks are summed at the pixel level. This reduces the computational complexity from exponential to linear, making the entire scheme practical for engineering applications.

[0079] To address the shortcomings of traditional iterative optimization algorithms, such as fixed parameters, slow convergence, and susceptibility to local optima, an intelligent optimization strategy based on the introspection mechanism of a dual-mode memristor is designed. This strategy draws upon the memory and introspection characteristics of memristors to construct a mathematical model containing "short-term memristor values" and "long-term memristor values," used to perceive the "immediate effect" and "long-term trend" of the iterative process in real time.

[0080] By combining the memristor introspection model with the Alternating Direction Multiplier Method (ADMM), closed-loop adaptive control of the optimization parameters is achieved. The regularization parameter in the ADMM algorithm is adjusted using the dual-mode memristor value. and penalty parameters By implementing collaborative, multi-mode dynamic updates, the algorithm can intelligently switch between "fast-forward convergence" and "cautious exploration" modes. This ensures convergence speed while effectively escaping local optima, significantly improving the algorithm's efficiency and robustness.

[0081] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," 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, 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.

[0082] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. An adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism, characterized in that: Includes the following steps: S1. Input a noisy image and construct a dynamic fractional-order guidance matrix for the image; specifically: calculate the local structural complexity of each pixel in the image based on multi-scale structural entropy, and label the complexity as a fractional-order unique to that pixel through a nonlinear mapping function, generating a dynamic fractional-order guidance matrix V with the same size as the noisy image; S2. Based on the dynamic fractional-order guidance matrix V, construct a dynamic fractional-order fully variational regularized model; specifically: decompose the variable-order fractional-order differential operation into multiple fixed-base kernels convolved with the standard image, and... And a pixel-level weighted summation of a dynamic weight mask generated by the dynamic fractional order guidance matrix V, and an energy functional containing a data fidelity term and a dynamic fractional total variation regularization term is constructed accordingly; S3, an optimization algorithm based on a dual-mode memristor introspection mechanism is used to solve the dynamic fractional total variation regularization model; specifically: a dual-mode memristor mathematical model containing short-term and long-term memristor values ​​is constructed to perceive the immediate effect and long-term trend of the iteration process, and the key parameters of the optimization algorithm are dynamically adjusted accordingly, and iterative solutions are performed to obtain the denoised image; S4. Determine whether the iteration process meets the preset convergence condition. If it does, output the final denoised image.

2. The adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism according to claim 1, characterized in that, Step S1 involves constructing a dynamic fractional-order guidance matrix, specifically including: S11, constructing an L-layer Gaussian pyramid for the input noisy image; S12, calculating the local entropy of each pixel in each layer of the pyramid; S13, upsampling the local entropy maps of each layer to the original image size and performing weighted fusion to generate a multi-scale structural entropy map HMSE(x,y); S14, using a nonlinear mapping function: The multi-scale structural entropy map HMSE(x,y) is mapped to the fractional order of each pixel, where vmax is the maximum order, HT is the entropy threshold adaptively determined by Otsu's method, α is the slope control parameter, and β is the offset correction parameter. This step yields a highly refined dynamic fractional order guidance matrix that is identical in size to the image. 。 3. The adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism according to claim 1, characterized in that, The specific implementation of step S2 is as follows: The fractional differential of order 1 is expressed as: Where Bj is a fixed set of basis difference kernels, J is the number of basis kernels, and Wj(v) is a dynamic weight mask that depends on order v, implemented through a pre-computed interpolation polynomial. Representing convolution operations; constructing the energy functional of the denoising model. The goal is to find the image that minimizes the functional. ： in The denoised image to be solved. The image contains noise; the first term on the right side of the equation is the data fidelity term. The first term is the regularization parameter; the second term is the dynamic fractional total variation regularization term. It is an L1 norm. It represents the Hadamardi (or Hadama) stack.

4. The adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism according to claim 3, characterized in that, The basis difference kernel includes a 0th-order identity operator, a 1st-order difference operator, and a 2nd-order Laplace operator, and the dynamic weight mask Wj(v) is a predefined polynomial function of order v.

5. The adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism according to claim 1, characterized in that, Step S3 involves constructing a mathematical model for a dual-mode memristor, specifically including: S31, based on the residual change from a single iteration. Update short-term memristor value Its update rules are as follows: Where σ(·) is the Sigmoid function, This is the short-term sensitivity coefficient; These are the preset maximum and minimum values ​​of the memristor, respectively; S32, update the long-term memristor value based on the stagnation indicator S(t) defined by the number of times the residual change is positive in the past Tw iterations. Its update rules are as follows: Where η is the long-term memory accumulation rate.

6. The adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism as described in claim 5, characterized in that: The key parameters of the dynamic adjustment optimization algorithm in step S3 are as follows: the optimization algorithm is the alternating direction multiplier method, and its key parameters include the regularization parameter λ and the penalty parameter ρ; the update of the regularization parameter λ is dominated by the short-term memristor value, and the rule is: The update of the penalty parameter ρ is jointly determined by the short-term memristor value and the long-term memristor value, according to the following rule: ;in, and Here, k is the basic parameter, and k is the long-term inhibition coefficient.

7. A storage device, characterized in that: The storage device stores instructions and data to implement the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism as described in any one of claims 1 to 6.

8. An adaptive image denoising device based on dynamic fractional order and memristor introspection mechanism, characterized in that: include: A processor and a storage device; the processor loads and executes instructions and data in the storage device to implement the adaptive image denoising method based on dynamic fractional order and memristor introspection mechanism as described in any one of claims 1 to 6.

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