An image restoration method and system for dynamic scattering medium imaging

Abstract

The application discloses an image restoration method and system for dynamic scattering medium imaging. The method is based on a low-frequency compensation and enhancement unit to process an original speckle image, correct illumination imbalance caused by scattering, and enhance local contrast. Based on a Fourier phase correction unit, the method performs Fourier transform on a corrected image, extracts an amplitude spectrum and a phase spectrum of the corrected image, performs two-dimensional phase unwrapping operation on the phase spectrum, and performs inverse Fourier transform on the unwrapped phase spectrum and the amplitude spectrum after recombination, to obtain a frequency domain corrected image, so as to correct phase distortion caused by dynamic scattering. The frequency domain corrected image is input into a trained image restoration model to obtain a restored image. The application combines intensity domain preprocessing based on physical principles and frequency domain phase correction to solve the image restoration problem under the condition of dynamic scattering.

Description

Technical Field

[0001] This invention relates to the field of image restoration technology, specifically to an image restoration method and system for imaging dynamic scattering media. Background Technology

[0002] Recovering high-fidelity images through dynamically scattering media remains one of the most enduring and cutting-edge challenges in optical physics and optical imaging. Despite decades of development, this challenge remains significant: when coherent or partially coherent light passes through non-uniform structures such as biological tissue, haze, or turbulent water, numerous random scattering events disrupt the light waves and produce seemingly random speckle patterns, obscuring all identifiable target features. This failure of deterministic light transmission fundamentally limits the ability to visualize and detect complex environments in situ, impacting fields such as biomedical diagnostics, environmental monitoring, remote sensing, and underwater exploration.

[0003] The core of this problem lies in the inherent high-dimensional randomness of multiple scattering. Each scattering event simultaneously perturbs the amplitude and phase of the wavefront. When the optical thickness reaches a certain level, the mapping from the target field to the detection intensity essentially becomes random. Traditional imaging architectures that rely on stable and reversible forward models thus fail. Recovering the target from speckle measurements containing only intensity becomes a severely ill-posed inverse problem, with its solution space dominated by nonlinearity, ambiguity, and rapid time decorrelation.

[0004] To overcome this obstacle, existing technologies have developed along two complementary paths. The first path employs a physics-driven strategy, explicitly modeling or manipulating the scattering process. Calibration-based methods attempt to directly characterize the scattering system. For example, the transfer matrix (TM) method aims to fully measure the linear input-output response of a static scattering layer, theoretically enabling accurate inversion. However, its practical application is limited by stringent calibration requirements and extreme sensitivity to micrometer-scale perturbations, making it infeasible in dynamic or biological environments. Some methods utilize statistical invariance techniques, such as speckle correlation and optical memory effect methods, which leverage angular or spatial invariance in the scattering process. However, their effectiveness rapidly decreases with increasing optical thickness or spatial decorrelation. Building upon these strategies, active compensation methods such as wavefront shaping actively modulate the incident field to counteract scattering distortion. While effective for static media, their iterative feedback loops are often too slow to track the temporal correlation characteristics of biological tissues or turbulent media. Therefore, these physics-driven methods still face a fundamental challenge: they typically cannot address the statistical drift caused by unpredictable variations in scattering intensity, microstructure, or dynamic fluctuations.

[0005] The second approach utilizes a data-driven method based on deep learning. By learning complex nonlinear mappings directly from large-scale paired datasets, deep learning models can implicitly invert the scattering process without requiring an explicit physics model. However, this method still suffers from a key limitation: the sensitivity of imaging performance to changes in scattering conditions and a lack of generalization ability. The scattering process is highly sensitive to variations in particle density, refractive index contrast, path length, and temporal fluctuations. Therefore, a network trained under one scattering condition often fails under another. This sensitivity reflects the inherent instability of imaging under dynamically changing scattering conditions, which remains a core challenge for practical deployment.

[0006] Given these limitations, existing technologies attempt to bridge this gap by incorporating physical priors into a data-driven framework. However, the iterative nature of these generative methods introduces significant computational overhead. Summary of the Invention

[0007] To address these issues, this invention proposes an image restoration method and system for imaging dynamic scattering media.

[0008] According to one aspect of the present invention, an image reconstruction method for imaging dynamic scattering media is proposed, comprising the following steps: S1, acquire the original image and the corresponding original speckle image; S2, the original speckle image is preprocessed by the low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model. The illumination-reflection physical model represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to the low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to the high-frequency structural information of the target image information. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. S3, based on the Fourier phase correction unit, the corrected image is subjected to frequency domain phase correction processing. The frequency domain phase correction processing includes: performing Fourier transform on the corrected image, extracting the amplitude spectrum and phase spectrum of the corrected image, performing a two-dimensional phase unwinding operation on the phase spectrum to obtain the unwound phase spectrum, synthesizing the amplitude spectrum and the unwound phase spectrum into a corrected spectral representation, and performing an inverse Fourier transform on the corrected spectral representation to obtain the frequency domain corrected image. S4, input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image; S5. The speckle image is restored based on the low-frequency compensation and enhancement unit, the Fourier phase correction unit, and the image restoration model.

[0009] This invention employs a dual-domain preprocessing architecture, consisting of a Low-Frequency Compensation and Enhancement Unit (LCEU) and a Fourier Phase Correction Unit (FPCU), arranged in an ordered cascade. First, the original speckle image undergoes intensity domain illumination correction and contrast enhancement. Then, the corrected image undergoes frequency domain phase deconvolution to correct phase distortion, resulting in a statistically stable frequency-domain corrected image that is input into the image reconstruction model. This invention combines the advantages of physical preprocessing with deep learning, effectively addressing the problem of neural network reconstruction performance degradation due to input distribution drift under dynamic scattering conditions. It improves the model's generalization ability and reconstruction stability under different scattering intensities.

[0010] Specifically, S2 includes: the low-frequency compensation and enhancement unit performs a logarithmic transformation on the original speckle image based on the illumination-reflection physical model to obtain a logarithmic domain image; after performing a Fourier transform on the logarithmic domain image, it uses a Gaussian high-pass filter to filter the logarithmic domain image after the Fourier transform; it performs an inverse Fourier transform and an exponential transform on the filtered spectrum to obtain an illumination normalized image; and it performs adaptive histogram equalization on the illumination normalized image to obtain the corrected image.

[0011] This invention filters the original speckle image based on the illumination-reflection physical model, separates and processes the illumination and reflection components in the logarithmic domain, and then enhances the local contrast through adaptive histogram equalization, which has clear physical interpretability.

[0012] Specifically, the transfer function of the Gaussian high-pass filter is: Where u and v represent the horizontal and vertical frequency coordinates, The cutoff frequency is used to determine the degree of low-frequency suppression.

[0013] This invention employs a Gaussian high-pass filter to perform homomorphic filtering on dynamic scattering speckle, and controls the degree of low-frequency suppression by the cutoff frequency parameter σ, thereby achieving adaptive attenuation of low-frequency illumination components under different scattering intensities.

[0014] Specifically, the image restoration model includes an encoder path, a decoder path, and an output unit. The encoder path includes multiple downsampling modules connected in sequence, used to progressively extract feature maps at multiple scales and expand the receptive field. The decoder path includes multiple upsampling modules corresponding to the multiple downsampling modules. Each upsampling module upsamples the feature map output by the previous upsampling module and concatenates and processes the feature map output by the corresponding downsampling module with the feature map output by the upsampling module. The output of the last upsampling module in the decoder path is processed by the output unit to generate the restored image.

[0015] This invention employs a multi-layer encoder-decoder structure for image reconstruction, which transmits high-frequency spatial details from each layer of the encoder to the decoder. This allows the network to utilize both deep semantic information and shallow detail information simultaneously. Combined with the statistical consistency input provided by the dual-domain preprocessing of the low-frequency compensation and enhancement unit and the Fourier phase correction unit, the network can suppress noise introduced by scattering while preserving the spatial structure information of the target.

[0016] Specifically, training the image restoration model based on the difference between the restored image and the original image in S4 includes: The image restoration model is trained by constructing a joint loss function based on the difference between the restored image and the original image. The joint loss function includes a mean squared error term (MSE) and a negative Pearson correlation coefficient term (NPCC), which is expressed as: L = MSE + NPCC. in, , , This refers to the restored image. This refers to the original image. and The average intensity of the restored image and the original image are respectively represented. Indicates the width of the image. Let L represent the height of the image, L represent the joint loss function, x represent the horizontal coordinate of the pixel, and y represent the vertical coordinate of the pixel.

[0017] This invention employs a joint loss function of mean square error and negative Pearson correlation coefficient to simultaneously constrain pixel-level intensity accuracy and global structural correlation during the training process.

[0018] Specifically, the image reconstruction model is trained based on a hybrid condition training strategy, wherein the hybrid condition training strategy includes: under multiple scattering intensity conditions within a preset range of scattering intensity variation, the original image and the corresponding original speckle image are collected respectively to obtain a hybrid dataset for training the image reconstruction model.

[0019] This invention employs a hybrid training strategy, collecting samples under multiple scattering intensities to form a hybrid training set for training a single image reconstruction model. This enables the model to learn image feature representations that remain unchanged when scattering intensities change, effectively eliminating the generalization error of traditional models when scattering conditions change.

[0020] Specifically, obtaining the original speckle image in S1 includes: The first beam is generated by the light source module; The original image is loaded using a spatial light modulator, and the first beam is phase-modulated. The phase-modulated first beam is incident on the dynamic scattering medium module, which includes a transparent container, a scattering medium disposed in the transparent container, and a stirring device. The stirring device is used to continuously stir to generate dynamic scattering conditions. The original speckle image is obtained by acquiring the light signal transmitted through the dynamic scattering medium module by an image sensor set on the light path side of the transparent container.

[0021] This invention comprises a light source module, a spatial light modulator, a dynamic scattering medium module, and an image sensor to form a complete speckle acquisition device. It uses a stirring device to continuously stir the scattering medium to generate dynamic scattering conditions, providing a paired dataset covering multiple scattering intensities for training the image reconstruction model, thus ensuring the integrity of model training and the reliability of reconstruction quality.

[0022] Specifically, S3 includes: For the corrected image Performing a Fourier transform yields the spectrum as follows: ,in, and The amplitude spectrum and the phase spectrum are respectively represented, and j represents an imaginary number; Perform a two-dimensional phase unwinding operation on the phase spectrum to obtain the unwound phase spectrum. , Represents the horizontal coordinate axis. Indicates the vertical coordinate axis; The amplitude spectrum and the unwinding phase spectrum are combined to form the corrected spectral representation. ; Finally, perform an inverse Fourier transform on the corrected spectral representation and take the modulus to obtain the frequency domain corrected image. , This indicates that an inverse Fourier transform is being performed.

[0023] According to one aspect of the present invention, an image restoration system for imaging dynamic scattering media using the method described in any one of the first aspects is proposed, comprising the following modules: The data acquisition module is configured to acquire the original image and the corresponding original speckle image; A low-frequency processing module is configured to preprocess the original speckle image based on a low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model, which represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to high-frequency structural information of the target image. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. The phase correction module is configured to perform frequency domain phase correction processing on the corrected image based on the Fourier phase correction unit. The frequency domain phase correction processing includes: performing a Fourier transform on the corrected image to extract the amplitude spectrum and phase spectrum of the corrected image; performing a two-dimensional phase unwinding operation on the phase spectrum to obtain an unwound phase spectrum; combining the amplitude spectrum and the unwound phase spectrum to synthesize a corrected spectral representation; and performing an inverse Fourier transform on the corrected spectral representation to obtain a frequency domain corrected image. The model training module is configured to input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image. The image restoration module is configured to restore the speckle image based on the low-frequency processing module, the phase correction module, and the model training module.

[0024] According to one aspect of the present invention, a computer program product is provided having a computer program stored thereon, which, when executed by a processor, performs the method as described in the first aspect.

[0025] The advantages of this invention are: Based on the illumination-reflection physical model and the principles of interference physics, this invention designs a low-frequency compensation and enhancement unit and a Fourier phase correction unit to address the two independent degradation mechanisms of illumination imbalance and phase distortion in dynamic scattering. The low-frequency compensation and enhancement unit decomposes the speckle pattern into illumination and reflection components and processes them separately. The Fourier phase correction unit extracts the intensity spectrum phase and restores its continuity through two-dimensional phase unwinding. Each processing step has a clear physical meaning, overcoming the lack of interpretability in existing black-box methods. The ordered cascaded architecture of the low-frequency compensation and enhancement unit and the Fourier phase correction unit transforms speckle patterns under different scattering intensities into feature representations with a statistically consistent distribution, effectively reducing the distribution shift between different scattering conditions. Combined with a hybrid condition training strategy, the single image reconstruction model maintains stable reconstruction performance under different scattering intensities, effectively eliminating the generalization error of traditional deep learning models that drastically degrades in performance when scattering conditions change. This invention employs an encoder-decoder architecture. The encoder extracts multi-scale semantic features and expands the receptive field through progressive downsampling, while the decoder splices high-frequency detail features from each layer of the encoder along the channel dimension via skip connections. This preserves the fine spatial structure of the target while avoiding overfitting and training difficulties caused by stacking deep networks. Compared to existing technologies that use complex models such as generative adversarial networks for post-processing enhancement, this invention features a simple and efficient network structure that directly receives statistically consistent input from dual-domain preprocessing, enabling it to learn more effective reconstruction mappings at a lower computational cost. Attached Figure Description

[0026] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and, together with the description, serve to explain the principles of the invention. Other embodiments and many anticipated advantages of the embodiments will be readily recognized as they become better understood through reference to the following detailed description. Elements in the drawings are not necessarily to scale. The same reference numerals refer to corresponding similar parts.

[0027] Figure 1 A schematic flowchart of an image restoration method for imaging of dynamic scattering media according to the present invention is shown; Figure 2 A flowchart illustrating the dual-domain preprocessing architecture based on a low-frequency compensation and enhancement unit and a Fourier phase correction unit is shown. Figure 3 The diagram shows a comparison of the original speckle image, the partial application of LCEU, and the full application of LCEU. Figure 4 The visualization results, corresponding intensity histograms, and Fourier amplitude spectra of the original speckle image after sequential processing by LCEU and FPCU are shown. Figure 5 The Fourier phase diagrams of the image spectra before and after FPCU processing are shown. Figure 6 A schematic diagram of the network architecture of an image restoration model according to the present invention is shown; Figure 7 The results of comprehensive image reconstruction using the method of this application under different scattering conditions are shown; Figure 8 The experimental results of testing a single training conditional model, a mixed training conditional model, and the method of this application under all scattering conditions are shown in the comparison graph. Figure 9 A schematic diagram of an image restoration system for imaging of dynamic scattering media according to the present invention is shown; Figure 10A schematic diagram of a computer system architecture suitable for implementing the embodiments of this application is shown. Detailed Implementation

[0028] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0029] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0030] Figure 1 An image restoration method for imaging dynamic scattering media is shown, comprising the following steps: S1, acquire the original image and the corresponding original speckle image; S2, the original speckle image is preprocessed by the low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model. The illumination-reflection physical model represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to the low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to the high-frequency structural information of the target image information. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. S3, based on the Fourier phase correction unit, the corrected image is subjected to frequency domain phase correction processing. The frequency domain phase correction processing includes: performing Fourier transform on the corrected image, extracting the amplitude spectrum and phase spectrum of the corrected image, performing a two-dimensional phase unwinding operation on the phase spectrum to obtain the unwound phase spectrum, synthesizing the amplitude spectrum and the unwound phase spectrum into a corrected spectral representation, and performing an inverse Fourier transform on the corrected spectral representation to obtain the frequency domain corrected image. S4, input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image; S5. The speckle image is restored based on the low-frequency compensation and enhancement unit, the Fourier phase correction unit, and the image restoration model.

[0031] Specifically, obtaining the original speckle image in S1 includes: The first beam is generated by the light source module; The original image is loaded using a spatial light modulator, and the first beam is phase-modulated. The phase-modulated first beam is incident on the dynamic scattering medium module, which includes a transparent container, a scattering medium disposed in the transparent container, and a stirring device. The stirring device is used to continuously stir to generate dynamic scattering conditions. The original speckle image is obtained by acquiring the light signal transmitted through the dynamic scattering medium module by an image sensor set on the light path side of the transparent container.

[0032] In a specific embodiment, the light source module includes a 635nm semiconductor laser for outputting a coherent beam. A beam expander and a polarizer are sequentially arranged along the output optical path of the laser. The beam expander expands the coherent beam output by the laser, and the polarizer linearly polarizes the expanded beam. A beam splitter is disposed in the output optical path of the polarizer to split the expanded and polarized linearly polarized coherent beam into a first beam.

[0033] The first beam is guided to a spatial light modulator, which is a phase-type spatial light modulator used to load the original image and phase-modulate the first beam. The phase-modulated first beam, carrying the original image information, is reflected by the spatial light modulator and returns to the beam splitter, and then incident on the dynamic scattering medium module.

[0034] The dynamic scattering medium module includes a transparent container and a scattering medium disposed within the transparent container. The transparent container is an acrylic water tank, and the scattering medium is skim milk, injected into the transparent container at a predetermined volume (60 ml to 120 ml). The transparent container is also equipped with a stirring device (magnetic stirrer) with a stirring speed of 1250 RPM, used to continuously stir the scattering medium during imaging to generate dynamic scattering conditions. By changing the volume of skim milk injected and continuously stirring, dynamic scattering environments with different scattering intensities can be created within the transparent container. The effective scattering intensity of the dynamic scattering medium is quantified using the percentage of milk volume added (v / v%), defined as: Scattering Intensity = ,in, This is the volume of skim milk. This refers to a fixed volume of water in a transparent container.

[0035] An image sensor is positioned on the outgoing light path of the transparent container at a distance of 10 cm from the transparent container. It is used to receive the light signal transmitted through the dynamic scattering medium and convert it into the original speckle image.

[0036] The original image and its corresponding original speckle image propagated through a dynamic scattering medium are displayed on the spatial light modulator. In this embodiment, a diverse dataset containing 4100 image pairs was created, including handwritten digits from the MNIST / EMNIST dataset and complex real-world targets, to evaluate generalization ability. For each milk volume, a separate complete dataset was generated. All images were preprocessed by cropping the central region of interest, downsampling to 128×128 pixels using a 4×4 block average, and normalizing the intensity to the [0,1] range.

[0037] Figure 2 A schematic flowchart of the dual-domain preprocessing architecture based on the Low Frequency Compensation and Enhancement Unit (LCEU) and Fourier Phase Correction Unit (FPCU) of the present invention is shown. Figure 2 As shown, the original speckle image before being input into the image reconstruction model. First, a deterministic non-learning preprocessing stage is adopted, which consists of a low-frequency compensation and enhancement unit and a Fourier phase correction unit connected in series.

[0038] The low-frequency compensation and enhancement unit (LCEU) is used to perform intensity domain preprocessing on the original speckle image to correct illumination imbalances caused by dynamic scattering and enhance local contrast. The specific processing procedure is as follows: First, the intensity of the original speckle image Modeled as lighting components With reflection component The product of: Among them, the lighting component Corresponding to the slowly changing low-frequency background, the reflection component This corresponds to high-frequency details related to the target structure. Under dynamic multiple scattering conditions, this separation serves as a practical approximation because scattering redistributes energy across different spatial frequency bands. x represents the horizontal coordinate of the pixel, and y represents the vertical coordinate of the pixel.

[0039] Taking a logarithmic transformation of the above model converts the multiplicative relationship into an additive form, resulting in a logarithmic domain image: In this model, the low-frequency components are mainly associated with slowly changing illumination-related intensity variations, while the higher-frequency components are associated with abrupt spatial variations and structural details.

[0040] Subsequently, a Fourier transform is performed on the logarithmic domain image, and a Gaussian high-pass filter is used for homomorphic filtering to attenuate the low-frequency illumination component caused by dynamic scattering. The transfer function of the Gaussian high-pass filter is: Where u and v represent the horizontal and vertical frequency coordinates, The cutoff frequency is used to determine the degree of low-frequency suppression. This filter suppresses slowly varying low-frequency intensity components while preserving spatial variations that contribute to structural contrast.

[0041] The filtered spectrum is returned to the spatial domain through inverse Fourier transform and exponential transform, and then normalized to obtain the illumination normalized image: ,in, This indicates that an inverse Fourier transform is being performed. This represents the filtered spectrum. This indicates an exponential transformation.

[0042] Filtering can compensate for global illumination variations, but contrast at local scales often remains weak. To address this limitation, Adaptive Histogram Equalization (AHE) is performed on the illumination-normalized image. This modifies local contrast based on the intensity distribution within each region, enhancing local structural details without introducing global artifacts or noise amplification. The final output of the LCEU is the corrected image. .

[0043] This process produces an illumination-normalized and contrast-enhanced image while improving the signal-to-interference ratio (SIR), making it suitable for subsequent processing stages. Homomorphic filtering and adaptive histogram equalization together improve the balance between low-frequency background variations and residual spatial structure, resulting in an enhanced speckle representation with improved spatial contrast and a more appropriate full-spectral distribution.

[0044] After LCEU completes intensity domain correction, the corrected image It is input to the Fourier Phase Correction Unit (FPCU) for frequency domain phase correction processing.

[0045] It should be clarified that the phase processed by the FPCU in this invention is the spectral phase of the recorded intensity image, rather than the optical phase of the scattered light field.

[0046] Specifically, the complex optical field after the light field propagates through a dynamic scattering medium can be written as: ,in and Let represent the amplitude and optical phase of the scattered light field, respectively. Since the image sensor only records the intensity distribution, the measured speckle image is as follows: Therefore, optical phase It cannot be directly obtained from the recorded intensity image. However, the recorded speckle intensity is formed by the interference of multiple scattered wave components. If the scattered field is represented as... N The superposition of scattering components: Then the measured intensity becomes: This expression indicates that although the optical phase is not directly measured, the recorded speckle intensity is modulated by the relative phase difference between the scattered light paths. Therefore, the Fourier phase extracted from the measured intensity spectrum represents the spectral phase of the intensity pattern generated by the interference process, rather than the phase of the physical light field itself.

[0047] Based on the above physical principles, the FPCU processes the LCEU-corrected image as follows: Given a corrected image Its spectrum is represented as: ,in, and Let represent the amplitude spectrum and the phase spectrum, respectively, where j represents an imaginary number. The phase spectrum... The intensity spectrum phase of the corrected image is distinct from the optical phase of the light field propagation.

[0048] In the Fourier representation of a speckle intensity image, due to the boundedness of the phase operator, the phase... Inherently wrapped in Within the interval. Under dynamic scattering conditions, the interference between multiple scattered wave components produces a highly irregular speckle intensity distribution, which manifests as abrupt discontinuities in the wrapped spectrum phase representation. To recover a continuous and regularized Fourier phase representation, a two-dimensional phase deconvolution operation is applied: , Represents the horizontal coordinate axis. Represents the vertical coordinate axis.

[0049] That is, first along the horizontal coordinate axis of the spatial frequency domain ( (axis) direction relative to the phase spectrum Perform one-dimensional phase unconvolution, then along the vertical coordinate axis ( Perform one-dimensional phase unconvolution in the axis direction to eliminate the phase principal values ​​in Artificial phase jumps caused by periodic truncation within the interval restore the continuity of the intensity spectrum phase, thus obtaining the unwound phase spectrum. .

[0050] Subsequently, the unwound continuous phase and the original amplitude spectrum are reconstructed into a corrected spectral representation: .

[0051] Finally, perform an inverse Fourier transform on the corrected spectral representation and take the modulus to obtain the frequency domain corrected image: .

[0052] This Fourier-domain phase regularization reduces abrupt discontinuities in the intensity spectrum phase and provides a more continuous spectral representation of the measured speckle intensity, thereby stabilizing the speckle representation provided to the image reconstruction model under different scattering conditions. FPCU complements LCEU by addressing phase-induced distortion, forming a complete preprocessing pipeline that improves the signal-to-interference ratio through complementary intensity-domain enhancement and Fourier spectral phase regularization.

[0053] Figure 3 The response of LCEU was evaluated using local root-mean-square contrast. The local contrast of the original speckle pattern decreased significantly as the medium became more turbid. After homomorphic filtering, full homomorphic filtering, and adaptive histogram equalization, the local contrast was significantly enhanced under all scattering conditions. This indicates that the two stages of LCEU have complementary effects: homomorphic filtering compensates for low-frequency background variations, while adaptive histogram equalization improves the visibility of residual local structures.

[0054] like Figure 4 As shown in (a), after applying homomorphic filtering and subsequent adaptive histogram equalization, the suppressed fine structural details in the original speckle are revealed, the contrast is improved, and the feature contours are clearer. Figure 4 (b) in the diagram quantizes the transformation. The histogram of the original speckle pattern exhibits a narrow-band skewed distribution concentrated in the midtones, indicating limited global contrast. After LCEU processing, the histogram is significantly broadened, indicating an improved signal-to-interference ratio and a more balanced and wider intensity range. The corresponding intensity histogram remains stable after FPCU processing, confirming that phase correction can be achieved without degrading the contrast enhancement provided by LCEU. Figure 4 The Fourier amplitude spectrum of (c) further demonstrates that the processed corrected image exhibits clearer spectral organization and sharper intensity transitions compared to the original speckle image input.

[0055] The subsequent FPCU stage, while maintaining the intensity characteristics established by LCEU, addresses phase-dependent distortion. For example... Figure 5 As shown in the Fourier phase map, after FPCU processing, the phase representation of the image spectrum becomes smoother and more ordered compared to its wrapped version, which is consistent with the suppression of phase irregularities introduced by the spectrum wrapping.

[0056] In summary, these results demonstrate that the sequential application of LCEU and FPCU produces a more structured and detail-preserving representation, providing a more stable and structured representation for subsequent image reconstruction under different scattering conditions.

[0057] Figure 6A schematic diagram of the network architecture of the image restoration model is shown. The image restoration model adopts an encoder-decoder architecture, and its input is the frequency-domain corrected image output by the FPCU. The output is a restored image. .

[0058] Specifically, the image reconstruction model adopts an encoder-decoder architecture. The encoder path includes four downsampling modules connected in sequence. Each downsampling module includes two convolutional units and a 2×2 max-pooling layer connected in sequence, used to progressively extract multi-scale feature representations and expand the receptive field. Each convolutional unit includes a 3×3 convolutional layer, a batch normalization layer, and a ReLU activation layer. The four downsampling modules output feature maps with spatial resolutions of 128×128, 64×64, 32×32, and 16×16, respectively.

[0059] The decoder path includes four upsampling modules corresponding to the four downsampling modules. Each upsampling module upsamples the feature map output by the previous upsampling module through a two-dimensional transposed convolutional layer, and then concatenates the feature map output by the corresponding downsampling module with the feature map of the upsampling module in the channel dimension through skip connections. The concatenated feature map is then processed by two convolutional units in sequence before being output. The output of the last upsampling module in the decoder path is processed by the output unit to generate a restored image with the same spatial resolution as the input. The output unit includes a 1×1 convolutional layer and a Sigmoid activation function.

[0060] The image restoration model is trained by constructing a joint loss function based on the difference between the restored image and the original image. The joint loss function includes a mean squared error term (MSE) and a negative Pearson correlation coefficient term (NPCC), which is expressed as: L = MSE + NPCC. in, , , This refers to the restored image. This refers to the original image. and The average intensity of the restored image and the original image are respectively represented. Indicates the width of the image. Let L represent the height of the image, L represent the joint loss function, x represent the horizontal coordinate of the pixel, and y represent the vertical coordinate of the pixel.

[0061] The NPCC term, together with the MSE term, participates in the optimization of network parameters during each gradient update, enabling the network to simultaneously optimize pixel-level accuracy and global structural correlation during training. Based on the differences between the reconstructed image and the original image, the parameters of the image reconstruction model are optimized through the joint loss function, allowing the image reconstruction model to learn the reconstruction mapping from the frequency-domain corrected image to the original image.

[0062] In a preferred embodiment, a hybrid condition training strategy is used to train the image reconstruction model. Specifically, the hybrid condition training strategy includes: under multiple scattering intensity conditions within a preset range of scattering intensity variations (e.g., dynamic scattering conditions corresponding to volumes of 60 ml, 70 ml, 80 ml, 90 ml, 100 ml, 110 ml, and 120 ml of skim milk), acquiring the original image and the corresponding original speckle image to obtain a hybrid dataset, and using the hybrid dataset to train the image reconstruction model. In a specific example, 340 training image pairs are selected from each scattering condition, totaling 2380 training image pairs to form the hybrid training set. The single image reconstruction model trained using this hybrid condition training strategy maintains stable reconstruction performance across the entire range of scattering intensity variations, effectively eliminating the generalization gap commonly found in traditional deep learning methods in scattering imaging.

[0063] Training and testing were performed separately under each scattering condition, such as Figure 7 As shown in the figure, the experimental results show that the milk volume increased from... Figure 7 (a) 60 ml to Figure 7 The speckle pattern obtained under scattering conditions of 120 ml (g) showed that, under low scattering intensities of 60–80 ml, the corresponding reconstructed images maintained high fidelity and fine details. Under moderate scattering conditions of 90–110 ml, although noise and slight distortion gradually appeared in the reconstructed images, the basic target structure could still be recovered. Even under the extreme scattering conditions of 120 ml, the method could still successfully reconstruct identifiable target content.

[0064] The structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), mean absolute error (MAE), and Pearson correlation coefficient (PCC) were used to evaluate the quality of the reconstructed image. Specifically, the SSIM measures the overall similarity between the reconstructed and original images in terms of brightness, contrast, and structure; the PSNR, calculated based on the mean square error (MSE) between pixels, measures the maximum fidelity of the reconstructed and original images in pixel-by-pixel grayscale values; the MAE is calculated by averaging the absolute differences between all corresponding pixels in the reconstructed and original images; and the PCC measures the strength of the linear correlation between the reconstructed and original images, assessing whether the overall grayscale trends of the two images change in tandem.

[0065] exist Figure 7 In the comparison of quantitative indicators in column (i), it can be seen that the structural similarity index SSIM, peak signal-to-noise ratio PSNR, mean absolute error MAE, and Pearson correlation coefficient PCC show a monotonically decreasing trend with the increase of scattering intensity, reflecting the loss of physical information caused by multiple scattering.

[0066] like Figure 8 As shown, the image reconstruction model trained under single scattering conditions (80 ml), the image reconstruction model trained using a hybrid condition training strategy, and the image reconstruction method of this application were tested under all scattering conditions. The image reconstruction method of this application integrates three modules: LCEU, FPCU, and the image reconstruction model.

[0067] Experimental results show that the model trained under a single scattering condition maintains stable generalization performance within a range of ±10 ml around its training condition. Beyond this window, performance exhibits gradual degradation rather than catastrophic failure, indicating that the method is robust to moderate scattering condition biases.

[0068] The model trained using a hybrid training strategy (collecting data under all scattering conditions from 60 to 120 ml to form a hybrid training set) maintains stable high-fidelity reconstruction performance under all scattering conditions. Quantitative analysis shows that the hybrid training strategy significantly outperforms the single-condition training strategy under all scattering conditions, and the performance curve remains flat throughout the entire scattering range, effectively eliminating the generalization gap commonly found in traditional deep learning methods in scattering imaging.

[0069] To quantify the contribution of each module in this invention, system ablation experiments were conducted on the following four configurations: DNN only (baseline model), FPCU+DNN, LCEU+DNN, and the method proposed in this application (LCEU+FPCU+DNN). All configurations were evaluated on an 80 ml test set.

[0070] Table 1 Comparison of Ablation Experiment Performance ; As shown in Table 1, the experimental results show that the baseline DNN-only configuration achieves moderate performance, indicating that traditional neural networks have difficulty directly learning complex scattering transformations.

[0071] Adding FPCU alone provides marginal improvements in PSNR and PCC, but SSIM and MAE are slightly below baseline, indicating that phase regularization alone is insufficient to stabilize local structural similarity and pixel-level accuracy when the input still contains illumination imbalances and contrast degradation.

[0072] The LCEU+DNN configuration showed more significant gains across all metrics, highlighting the key role of contrast enhancement and illumination normalization.

[0073] The method in this application achieved the best performance across all metrics: SSIM improved to 0.9701, PSNR improved to 32.5979 dB, MAE decreased to 0.01124, and PCC improved to 0.9719. Ablation studies further support the necessity and effectiveness of the phase unwinding step. While applying the FPCU directly to the raw speckle intensity alone provides some improvement, the complete LCEU+FPCU preprocessing step achieved the best reconstruction performance across all configurations. This indicates that phase unwinding is more effective when applied after intensity normalization and contrast enhancement, confirming its role in generating a more stable and informative speckle intensity reconstructed intensity spectrum phase representation.

[0074] Compared to the baseline configuration, the method in this application achieves a relative improvement of approximately 5.7% in SSIM, approximately 8.6% in PSNR, and approximately 42% in MAE. This synergistic improvement demonstrates that LCEU and FPCU address complementary physical limitations: LCEU corrects intensity domain degradation, and FPCU stabilizes Fourier phase distortion. The combined effect of these two approaches creates a structurally consistent input space, enabling the image reconstruction model to learn more effective mappings.

[0075] In one specific example, the image reconstruction model employs the Adam optimizer with an initial learning rate of 10. -3 The training run consisted of 50 rounds. All experiments were performed on a workstation equipped with an NVIDIA GeForce RTX 3090 GPU (24 GB VRAM). The low-frequency compensation and enhancement unit and the Fourier phase correction unit were implemented using OpenCV 4.7.0, and the neural network was built using TensorFlow 2.11.0 and Keras 2.11.0.

[0076] According to one aspect of the present invention, an image reconstruction system for imaging dynamic scattering media using the method described in any one of the first aspects is proposed, such as... Figure 9 As shown, it includes the following modules: The data acquisition module 901 is configured to acquire the original image and the corresponding original speckle image; The low-frequency processing module 902 is configured to preprocess the original speckle image based on the low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model, which represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to high-frequency structural information of the target image information. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. The phase correction module 903 is configured to perform frequency domain phase correction processing on the correction image based on the Fourier phase correction unit. The frequency domain phase correction processing includes: performing a Fourier transform on the correction image, extracting the amplitude spectrum and phase spectrum of the correction image, performing a two-dimensional phase unwinding operation on the phase spectrum to obtain an unwound phase spectrum, synthesizing the amplitude spectrum and the unwound phase spectrum into a corrected spectral representation, and performing an inverse Fourier transform on the corrected spectral representation to obtain a frequency domain corrected image. The model training module 904 is configured to input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image. The image restoration module 905 is configured to restore the speckle image based on the low-frequency processing module, the phase correction module and the model training module.

[0077] The following is for reference. Figure 10 It shows a schematic diagram of the structure of a computer system 1000 suitable for implementing electronic devices according to embodiments of the present application. Figure 10 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0078] like Figure 10 As shown, the computer system 1000 includes a central processing unit (CPU) 1001, which performs various appropriate actions and processes based on programs stored in read-only memory (ROM) 1002 or programs loaded from storage section 1008 into random access memory (RAM) 1003. The RAM 1003 also stores various programs and data required for the operation of the system 1000. The CPU 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0079] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a liquid crystal display (LCD) and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card and a modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 1010 as needed so that computer programs read from it can be installed into storage section 1008 as needed.

[0080] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts are implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program is downloaded and installed from a network via communication section 1009, and / or installed from removable medium 1011. When the computer program is executed by central processing unit (CPU) 1001, it performs the functions defined in the methods of this application.

[0081] It should be noted that the computer-readable storage medium of this application is a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium is, for example—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium is any tangible medium that contains or stores a program used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium includes a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals take various forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium or any computer-readable storage medium other than a computer-readable storage medium may transmit, propagate, or transfer a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0082] Computer program code for performing the operations of this application is written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code executes entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer is connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or connected to an external computer (e.g., via the Internet using an Internet service provider).

[0083] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram represents a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually execute substantially in parallel, and they may sometimes execute in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, is implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0084] The modules described in the embodiments of this application are implemented in software or hardware.

[0085] On the other hand, this application also provides a computer-readable storage medium included in the electronic device described in the above embodiments; or existing independently and not assembled into the electronic device. The computer-readable storage medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform: S1, acquiring an original image and a corresponding original speckle image; S2, preprocessing the original speckle image based on a low-frequency compensation and enhancement unit to obtain a corrected image, wherein the low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model, the illumination-reflection physical model representing the original speckle image as a product of an illumination component and a reflection component, the illumination component corresponding to low-frequency background changes caused by dynamic scattering, and the reflection component corresponding to high-frequency structural information of the target image information, the low-frequency compensation and enhancement unit obtaining the corrected image by suppressing the illumination component and enhancing local contrast. S3, perform frequency domain phase correction processing on the corrected image based on the Fourier phase correction unit. The frequency domain phase correction processing includes: performing a Fourier transform on the corrected image to extract the amplitude spectrum and phase spectrum of the corrected image; performing a two-dimensional phase unwinding operation on the phase spectrum to obtain an unwound phase spectrum; synthesizing the amplitude spectrum and the unwound phase spectrum into a corrected spectral representation; and performing an inverse Fourier transform on the corrected spectral representation to obtain a frequency domain corrected image. S4, input the frequency domain corrected image into an image restoration model to obtain a restored image; and train the image restoration model based on the difference between the restored image and the original image. S5, restore the speckle image based on the low-frequency compensation and enhancement unit, the Fourier phase correction unit, and the image restoration model.

[0086] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. An image reconstruction method for imaging dynamic scattering media, characterized in that, Includes the following steps: S1, acquire the original image and the corresponding original speckle image; S2, the original speckle image is preprocessed by the low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model. The illumination-reflection physical model represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to the low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to the high-frequency structural information of the target image information. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. S3, based on the Fourier phase correction unit, the corrected image is subjected to frequency domain phase correction processing. The frequency domain phase correction processing includes: performing Fourier transform on the corrected image, extracting the amplitude spectrum and phase spectrum of the corrected image, performing a two-dimensional phase unwinding operation on the phase spectrum to obtain the unwound phase spectrum, synthesizing the amplitude spectrum and the unwound phase spectrum into a corrected spectral representation, and performing an inverse Fourier transform on the corrected spectral representation to obtain the frequency domain corrected image. S4, input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image; S5. The speckle image is restored based on the low-frequency compensation and enhancement unit, the Fourier phase correction unit, and the image restoration model.

2. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, S2 specifically includes: A logarithmic transformation is performed on the original speckle image to separate the low-frequency components corresponding to the illumination component and the high-frequency components corresponding to the reflection component in the logarithmic domain of the original speckle image; Perform a Fourier transform on the logarithmically transformed image, and use a Gaussian high-pass filter to filter the frequency domain signal after the Fourier transform in order to attenuate the low-frequency components corresponding to the illumination component. Perform an inverse Fourier transform and an exponential transform on the filtered spectrum to obtain the illumination-normalized image; An adaptive histogram equalization process is performed on the illumination-normalized image to enhance local contrast and obtain the corrected image.

3. The image reconstruction method for imaging dynamic scattering media according to claim 2, characterized in that, The transfer function of the Gaussian high-pass filter is: Where u and v represent the horizontal and vertical frequency coordinates, The cutoff frequency is used to determine the degree of low-frequency suppression.

4. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, The image restoration model includes an encoder path, a decoder path, and an output unit. The encoder path includes multiple downsampling modules connected in sequence, used to progressively extract feature maps at multiple scales and expand the receptive field. The decoder path includes multiple upsampling modules corresponding to the multiple downsampling modules. Each upsampling module upsamples the feature map output by the previous upsampling module and concatenates and processes the feature map output by the corresponding downsampling module and the feature map output by the upsampling module. The output of the last upsampling module in the decoder path is processed by the output unit to generate the restored image.

5. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, S4 specifically includes training the image restoration model based on the difference between the restored image and the original image, which specifically includes: The image restoration model is trained by constructing a joint loss function based on the difference between the restored image and the original image. The joint loss function includes a mean squared error term (MSE) and a negative Pearson correlation coefficient term (NPCC), which is expressed as: L = MSE + NPCC. in, , , This refers to the restored image. This refers to the original image. and The average intensity of the restored image and the original image are respectively represented. Indicates the width of the image. Let L represent the height of the image, L represent the joint loss function, x represent the horizontal coordinate of the pixel, and y represent the vertical coordinate of the pixel.

6. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, The image reconstruction model is trained based on a hybrid condition training strategy, wherein the hybrid condition training strategy specifically includes: acquiring the original image and the corresponding original speckle image under multiple scattering intensity conditions within a preset range of scattering intensity variation to obtain a hybrid dataset for training the image reconstruction model.

7. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, S1 specifically includes obtaining the original speckle image: The first beam is generated by the light source module; The original image is loaded using a spatial light modulator, and the first beam is phase-modulated. The phase-modulated first beam is incident on the dynamic scattering medium module, which includes a transparent container, a scattering medium disposed in the transparent container, and a stirring device. The stirring device is used to continuously stir to generate dynamic scattering conditions. The original speckle image is obtained by acquiring the light signal transmitted through the dynamic scattering medium module using an image sensor located on the light path of the transparent container.

8. The image reconstruction method for imaging dynamic scattering media according to claim 1, characterized in that, S3 specifically includes: For the corrected image Performing a Fourier transform yields the spectrum as follows: ,in, and The amplitude spectrum and the phase spectrum are respectively represented, and j represents an imaginary number; Perform a two-dimensional phase unwinding operation on the phase spectrum to obtain the unwound phase spectrum. , Represents the horizontal coordinate axis. Indicates the vertical coordinate axis; The amplitude spectrum and the unwinding phase spectrum are combined to form the corrected spectral representation. ; Finally, perform an inverse Fourier transform on the corrected spectral representation and take the modulus to obtain the frequency domain corrected image. , This indicates that an inverse Fourier transform is being performed.

9. An image reconstruction system for imaging dynamic scattering media using the method described in any one of claims 1-8, characterized in that, Includes the following modules: The data acquisition module is configured to acquire the original image and the corresponding original speckle image; A low-frequency processing module is configured to preprocess the original speckle image based on a low-frequency compensation and enhancement unit to obtain a corrected image. The low-frequency compensation and enhancement unit processes the original speckle image based on an illumination-reflection physical model, which represents the original speckle image as a product of an illumination component and a reflection component. The illumination component corresponds to low-frequency background changes caused by dynamic scattering, and the reflection component corresponds to high-frequency structural information of the target image. The low-frequency compensation and enhancement unit obtains the corrected image by suppressing the illumination component and enhancing local contrast. The phase correction module is configured to perform frequency domain phase correction processing on the corrected image based on the Fourier phase correction unit. The frequency domain phase correction processing includes: performing a Fourier transform on the corrected image to extract the amplitude spectrum and phase spectrum of the corrected image; performing a two-dimensional phase unwinding operation on the phase spectrum to obtain an unwound phase spectrum; combining the amplitude spectrum and the unwound phase spectrum to synthesize a corrected spectral representation; and performing an inverse Fourier transform on the corrected spectral representation to obtain a frequency domain corrected image. The model training module is configured to input the frequency domain corrected image into the image restoration model to obtain the restored image, and train the image restoration model based on the difference between the restored image and the original image. The image restoration module is configured to restore the speckle image based on the low-frequency processing module, the phase correction module, and the model training module.

10. A computer program product, characterized in that, It stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1-8.

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