Scattering imaging image reconstruction method based on wavelet domain double-fraction matching model

Abstract

The invention discloses a scattering imaging image reconstruction method based on a wavelet domain double-fractional matching model, which comprises the following steps of: extracting full-frequency and high-frequency prior information of a target object by utilizing a trained full-frequency fractional matching sub-model and a trained high-frequency fractional matching sub-model; a speckle image, obtained by an image sensor, of a target object behind a scattering medium is subjected to Wiener deconvolution, support domain constraint and bilateral filtering processing and then serves as a fidelity term, image reconstruction is carried out, and the reconstruction process comprises noise input, prediction, correction, image segmentation, sub-image updating, sub-image merging, inverse wavelet transformation and denoising. And outputting a reconstructed image after taking the denoised image as an input and repeating the reconstruction process for the number of times of prediction. According to the method, the target object behind the scattering medium is reconstructed through efficient cooperation of high-dimensional low-rank prior information constraint and data fidelity, the problem of complex target object reconstruction in a scattering medium scene can be effectively solved, and the imaging quality is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of electronic information technology, and particularly to a scattering imaging image reconstruction method based on a wavelet domain bifractional matching model. Background Art

[0002] In many critical fields such as medical imaging, deep-sea exploration, and national defense security, imaging technologies through scattering media are playing a crucial role. In these complex application scenarios, the propagation path of light is often interfered by scattering media (such as fog, smoke, biological tissues, etc.), resulting in random refraction. This phenomenon not only makes direct imaging extremely difficult, but also seriously affects the image quality, greatly limiting the performance of the imaging system.

[0003] Existing scattering imaging schemes mainly include pure hardware schemes, algorithmic schemes, and diffusion model-based schemes.

[0004] Pure hardware scheme: Digital optical phase conjugation technology uses multiple digital components such as electro-optic modulators and spatial light modulators to generate phase conjugate light, and then realizes focusing and imaging through the scattering medium.

[0005] Algorithmic schemes: Traditional image reconstruction methods, such as traditional deconvolution, mainly perform deconvolution on the observed image using the point spread function of the measurement system.

[0006] Diffusion model-based scheme: The diffusion model is used to process the observed image.

[0007] In the process of implementing the technical solution of the present invention, the inventors of this patent have at least found the following technical problems in the prior art: (1) Pure hardware scheme: The increase of multiple digital components in digital optical phase conjugation technology often leads to an extremely complex imaging system, restricting the actual application scope.

[0008] (2) Algorithmic schemes: Traditional image reconstruction methods mainly reconstruct simple objects, and the lack of prior information constraints often leads to artifacts and noises being introduced into the reconstructed image.

[0009] (3) Diffusion model-based scheme: Although the diffusion model has greatly improved in image processing, it cannot effectively recover complex objects behind the scattering medium. Such schemes still do not solve the problem of how to combine physical models and more efficiently mine prior information.

[0010] In summary, most of the existing scattering imaging schemes focus on optimizing the imaging effect of simple objects, and there is still a large gap between them and the imaging requirements of complex objects in actual scenarios, unable to meet the actual imaging needs. Summary of the Invention

[0011] The scattering imaging image reconstruction method based on the wavelet domain double fractional matching model provided by the present invention can extract the high-dimensional low-rank prior information of the target object by the trained full-frequency fractional matching sub-model and high-frequency fractional matching sub-model, including full-frequency and high-frequency prior information, and reconstruct the target object behind the scattering medium through the efficient cooperation of the high-dimensional low-rank prior information constraint and data fidelity. It can effectively penetrate the scattering medium and obtain clear images, solve the problem that most of the existing scattering imaging schemes focus on optimizing the imaging effect of simple target objects and cannot meet the imaging requirements of complex target objects in actual scenarios, and significantly improve the imaging quality.

[0012] The present invention provides a scattering imaging image reconstruction method based on a wavelet domain double fractional matching model, and the method includes: In the prior information extraction stage, use the trained full-frequency fractional matching sub-model and high-frequency fractional matching sub-model to extract the full-frequency and high-frequency prior information of the target object; In the image reconstruction stage, under the double constraints of full-frequency and high-frequency prior information, take the speckle image of the target object behind the scattering medium obtained by the image sensor after Wiener deconvolution, support domain constraint and bilateral filtering processing as the fidelity term, and perform image reconstruction. The reconstruction process includes: The first step is to randomly generate four two-dimensional Gaussian noise images; The second step is to input the Gaussian noise image into the full-frequency fractional matching sub-model for image reconstruction; The third step is to introduce the constraint of full-frequency prior information, and at the same time use the fidelity term to enhance data consistency to obtain a predicted image; The fourth step is to use the annealed Langevin equation as a corrector and the fidelity term as a data consistency maintainer, and input the predicted image into the internal loop for correction to obtain an image to be reconstructed; The fifth step is to divide the image to be reconstructed into a high-frequency component original image and a low-frequency component original image; The sixth step is to input the high-frequency component original image into the high-frequency fractional matching sub-model, and use the high-frequency prior information for constraint, and at the same time use the fidelity term as a data consistency maintainer for fidelity to obtain a high-frequency component updated image; The seventh step is to perform weighted summation of the high-frequency component updated image and the high-frequency component original image, then merge and optimize with the low-frequency component original image, perform inverse wavelet transform and total variation regularization term denoising on the optimized wavelet domain image to obtain a denoised spatial domain image; The eighth step is to re-use the denoised spatial domain image after wavelet processing as the input, repeat the second to seventh steps for a preset number of times and then end the loop, and use the spatial domain image output after the last loop as the reconstructed image similar to the target object.

[0013] One or more technical solutions provided by the present invention have at least the following technical effects or advantages: By accurately capturing the high-dimensional low-rank prior information of the target object (including full-frequency and high-frequency prior information) as a constraint, the present invention takes the speckle image of the target object behind the scattering medium collected by the image sensor, which has been processed by Wiener deconvolution, support domain constraint, and bilateral filtering, as the fidelity term, and reconstructs the target object behind the scattering medium through the efficient cooperation of high-dimensional low-rank prior information constraint and data fidelity. During the image reconstruction process, through a series of collaborative optimization steps, it is ensured that the reconstructed image achieves the best balance between high-dimensional low-rank prior information constraint and data fidelity. The present invention effectively solves the problem of reconstructing complex target objects in the scattering medium scenario and significantly improves the imaging quality. Compared with the existing pure hardware solutions, the present invention does not require the use of multiple digital components, only needs to use an image sensor as a linear scattering imaging system, the imaging system is simple, and the application range is wide. Compared with the existing algorithm-based solutions and diffusion model-based solutions, when the present invention reconstructs complex target objects behind the scattering medium, the generated image artifacts are significantly reduced, the details are clearer and richer, and the overall quality is greatly improved. The present invention not only meets the high-precision requirements in complex imaging environments but also effectively bridges the gap between existing technologies and practical applications, providing reliable technical support for the efficient reconstruction of complex target objects.

[0014] The present invention has made a significant breakthrough in the reconstruction effect of complex target objects under the scattering medium. Experimental results prove that compared with the images obtained by the existing diffusion model-based solutions, the peak signal-to-noise ratio of the finally output reconstructed image of the present invention is increased by nearly 2.67 dB, and the structural similarity value reaches 0.7136, significantly improving the overall quality of the image. Description of the Drawings

[0015] Figure 1 It is the optical path schematic diagram of the linear scattering imaging system in an embodiment of the present invention; Figure 2 It is the flow chart of the scattering imaging image reconstruction method based on the wavelet domain double-fraction matching model in an embodiment of the present invention; Figure 3 It is the result diagram of simulation experiments using three different methods in an embodiment of the present invention; In the figure, sub-model 1 represents the full-frequency fraction matching sub-model, sub-model 2 represents the high-frequency fraction matching sub-model, P represents the predictor, C represents the corrector, DC represents the data consistency maintainer, and TV represents the total variation regularization term. Detailed Embodiments

[0016] The scattering imaging image reconstruction method based on the wavelet-domain double fractional matching model provided by the present invention can train and generate a full-frequency fractional matching sub-model and a high-frequency fractional matching sub-model to extract the high-dimensional low-rank prior information of the target object, including full-frequency and high-frequency prior information, and reconstruct the target object behind the scattering medium through the efficient cooperation of the high-dimensional low-rank prior information constraint and data fidelity. It can effectively penetrate the scattering medium and obtain clear images, solving the problem that most existing scattering imaging schemes focus on optimizing the imaging effect of simple target objects and cannot meet the imaging requirements of complex target objects in actual scenarios, and significantly improving the imaging quality.

[0017] First, the technical terms in the present invention are explained.

[0018] The wavelet-domain double fractional matching model is a prior learning model proposed in the present invention for the field of scattering imaging to solve the problem of insufficient extraction of prior information of single-channel spatial domain data. Through wavelet transform, the original single-channel training data is decomposed into four-channel full-frequency transform domain data and three-channel high-frequency transform domain data. On this basis, the fractional matching model is trained for the four-channel full-frequency transform domain data and the three-channel high-frequency transform domain data respectively, and finally a four-channel wavelet-domain full-frequency fractional matching sub-model (abbreviated as full-frequency fractional matching sub-model) and a three-channel wavelet-domain high-frequency fractional matching sub-model (abbreviated as high-frequency fractional matching sub-model) are obtained. The wavelet-domain double fractional matching model can efficiently learn the high-dimensional low-rank prior information of the target object to extract the high-dimensional low-rank prior information from complex data and accurately capture its global and local features.

[0019] Prior information extraction is to learn the physical characteristics such as image edges, textures, and shapes from a large number of image datasets. In the present invention, the proposed wavelet-domain double fractional matching model can extract the high-dimensional low-rank prior information of the target object, provide accurate and effective regularization constraints for the image reconstruction process, effectively suppress the phenomenon of model overfitting, and significantly improve the accuracy and stability of image reconstruction. Among them, the full-frequency prior information is a kind of high-dimensional low-rank prior information extracted from the target object by the full-frequency fractional matching sub-model, and the present invention uses the full-frequency prior information to constrain the generation of the image to be reconstructed. The high-frequency prior information is a kind of high-dimensional low-rank prior information extracted from the target object by the high-frequency fractional matching sub-model. The present invention uses the high-frequency prior information to enhance the detail and edge information of the image. Through the dual constraints of the full-frequency prior information and the high-frequency prior information, the high-quality reconstruction of complex target objects is realized.

[0020] Next, the linear scattering imaging system involved in the present invention is introduced.

[0021] Scattering imaging is an imaging technique that uses speckle information to reconstruct the object behind the scattering medium. Compared with traditional pure hardware solutions that require multiple digital components such as electro-optic modulators and spatial light modulators, the present invention constructs a linear scattering imaging system that only requires an image sensor. Its optical path principle is as follows Figure 1 shown. The light emitted by the LED passes through the collimating lens and then irradiates the target object. When the target light field passes through the scattering medium (such as fog, smoke, biological tissue, etc.), the light will undergo multiple scatterings. Finally, the speckle image captured by the image sensor can be regarded as the point spread function of the linear scattering imaging system convolved with the target object That is where represents the convolution operator. By measuring the point spread function and the speckle image of the system with the image sensor, the scattering imaging image reconstruction can be realized by means of deconvolution. However, there are many artifact interferences and low clarity in the reconstructed image without constraints. Therefore, the present invention needs to reconstruct the object behind the scattering medium through the efficient cooperation of high-dimensional low-rank prior information constraint and data fidelity to obtain a clear image.

[0022] To better understand the scattering imaging image reconstruction method based on the wavelet domain double fractional matching model of the present invention, the following will be described in detail in conjunction with the accompanying drawings of the specification and specific embodiments. Obviously, the embodiments described in the present invention are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0023] The scattering imaging image reconstruction method based on the wavelet domain double fractional matching model of the present invention mainly includes three stages, namely the model training stage, the prior information extraction stage, and the image reconstruction stage.

[0024] (1) Model training stage; In the model training stage, first use wavelet transform to convert the single-channel spatial domain image dataset of the target object into a four-channel full-frequency image dataset in the wavelet domain and a three-channel high-frequency image dataset in the wavelet domain, and then use the two datasets obtained after wavelet transform to train the first original fractional matching model and the second original fractional matching model respectively to obtain the trained full-frequency fractional matching sub-model and high-frequency fractional matching sub-model.

[0025] It should be noted that the wavelet basis function used in the wavelet transform process in this embodiment is the Haar function. In practical applications, there is no restriction on the selected wavelet basis function.

[0026] Among them, for the construction process of the full-frequency image dataset in the four-channel wavelet domain and the high-frequency image dataset in the three-channel wavelet domain, in the specific construction process, for example: select the LSUN-Church dataset as the original dataset of the target object, crop and adjust each selected image in the original dataset to 56×56 pixels, and then, with the adjusted image as the center, uniformly fill the black background area around it. Finally, generate a single-channel spatial domain image with a size of 256×256 pixels to complete the preprocessing of the original dataset. Next, select 10,000 images from the preprocessed dataset, and use wavelet transform to convert these 10,000 single-channel spatial domain images into the full-frequency image dataset in the four-channel wavelet domain and the high-frequency image dataset in the three-channel wavelet domain , where 、 、 、 respectively represent the low-frequency-low frequency sub-band image data subset, low-frequency-high frequency sub-band image data subset, high-frequency-low frequency sub-band image data subset, and high-frequency-high frequency sub-band image data subset obtained after wavelet transform of the single-channel spatial domain image dataset .

[0027] After constructing the full-frequency image dataset in the four-channel wavelet domain and the high-frequency image dataset in the three-channel wavelet domain , start to execute the training process, and the training process includes steps S11 to S13

[0028] Step S11: Input the full-frequency image dataset in the four-channel wavelet domain into the first original score matching model for training to learn the full-frequency prior information of the overall structure of the image and obtain the full-frequency score matching sub-model

[0029] Among them, the process of obtaining the full-frequency score matching sub-model includes steps S111 to S112

[0030] Step S111: Configure the stochastic differential equation with exploding variance used in the model training stage, and the expression is as follows , In the formula represents the full-frequency image dataset in the four-channel wavelet domain represents the full-frequency monotonically increasing function represents the full-frequency diffusion coefficient is the uniformly sampled time represents at Brownian motion in the dimensional real number space represents the vector dimension

[0031] The stochastic differential equation with exploding variance can effectively disperse the data distribution over a wide range of noise levels, enabling more effective learning of the underlying data structure and improving the quality of the generated samples.

[0032] Step S112: Through training, use the full-frequency continuous-time correlation score function to estimate the gradient of the full-frequency log data distribution . Considering that the true value is still unknown, choose to use instead of .

[0033] The process of using the full-frequency continuous-time correlation score function to estimate the gradient of the replaced full-frequency log data distribution is modeled as solving the following full-frequency core objective function in the context of a score-based stochastic differential equation: , where, represents the optimal parameters for full-frequency neural network training, represents the full-frequency neural network training parameters, represents the expectation, represents the positive weight function, represents the full-frequency image training samples for the four-channel wavelet domain, is a full-frequency Gaussian perturbation kernel centered on represents the full-frequency continuous-time correlation score function, is the full-frequency log data distribution gradient of

[0034] Step S12: Input the high-frequency image dataset in the three-channel wavelet domain into the second original score matching model for training to learn the high-frequency prior information of the image local details and texture features, and obtain the high-frequency score matching sub-model.

[0035] Among them, the process of obtaining the high-frequency score matching sub-model includes steps S121 to S122.

[0036] Step S121: Configure the stochastic differential equation with exploding variance used in the model training stage, and the expression is as follows: , where, represents the high-frequency image dataset in the three-channel wavelet domain, represents the high-frequency monotonically increasing function, represents the high-frequency diffusion coefficient, is the uniform sampling time, represents Brownian motion in the -dimensional real number space, represents a real number, represents the vector dimension.

[0037] The stochastic differential equation with variance explosion can effectively disperse the data distribution into a wide range of noise levels, enabling more effective learning of the underlying data structure and improving the quality of the generated samples.

[0038] Step S122: Through training, use the high-frequency continuous-time related score function to estimate the gradient of the high-frequency log data distribution . Considering that the true value of is still unknown, choose to use instead of .

[0039] The process of using the high-frequency continuous-time related score function to estimate the gradient of the replaced high-frequency log data distribution is modeled as solving the following high-frequency core objective function in the environment of the score-based stochastic differential equation: , where, represents the optimal parameters for high-frequency neural network training, represents the high-frequency neural network training parameters, represents the expectation, represents the positive weight function, represents the training samples of high-frequency images in the three-channel wavelet domain, is a high-frequency Gaussian perturbation kernel centered on, represents the high-frequency continuous-time related score function, is the high-frequency log data distribution gradient of.

[0040] Step S13: Configure the training parameters. First, add Gaussian noise to perturb the data distribution. For example, add 2000 Gaussian noise values between 0.01 and 384. Secondly, use the Adam optimizer for optimization. For example, set the learning rate of the Adam optimizer to 0.0002. Finally, set the number of iterations. For example, set the number of iterations to 500,000 times.

[0041] (2) Prior information extraction stage; As Figure 2 shown, in the prior information extraction stage, use the full-frequency score matching submodel trained in the model training stage (i.e.,Figure 2 The sub-model 1) and the high-frequency fractional matching sub-model (i.e., Figure 2 the sub-model 2) in

[0042] (III) Image reconstruction stage; As Figure 2 shown, in the image reconstruction stage, under the dual constraints of full-frequency and high-frequency prior information, the speckle image of the object behind the scattering medium acquired by the image sensor is used as the fidelity term after Wiener deconvolution, support domain constraint, and bilateral filtering to perform image reconstruction.

[0043] Among them, in order to further improve the underlying physical consistency of the reconstructed image and considering the existence of the region of interest in the actual imaging field, the speckle image is not directly used as the fidelity term, but the acquired speckle image needs to be processed by Wiener deconvolution, support domain constraint, and bilateral filtering and then used as the fidelity term . The fidelity term acts as a data consistency maintainer (i.e., Figure 2 the DC in ) during the entire reconstruction process. The processing of the acquired speckle image

[0044] specifically includes steps S21 to S22. Step S21: After processing the speckle image using Wiener deconvolution, the deconvolved image is obtained, and its expression is as follows: In the formula, is the deconvolved image, represents the Fourier transform, is the speckle image, is the point spread function in the Fourier domain, is 's conjugate, represents the adjustable parameter of the noise; Step S22: Perform support domain constraint and bilateral filtering on the deconvolved image to obtain the fidelity term , and the expression is as follows: , In the formula, represents a certain pixel position on the deconvolved image , represents the deconvolved image Another pixel position on Represents the fidelity term The pixel in The pixel value at Represents the deconvolved image The pixel in The pixel value at Represents the deconvolved image The pixel in The pixel value at Is the normalization factor used to ensure that the weights sum to 1 Is the pixel Neighborhood of Is the Gaussian function in the spatial domain Is the standard deviation in the spatial domain Is the Gaussian function in the intensity domain Is the standard deviation in the intensity domain Is the region of interest in the actual imaging field.

[0045] Among them, the reconstruction process includes the first step to the eighth step.

[0046] The first step is to randomly generate four two-dimensional Gaussian noise images.

[0047] The second step is to input the Gaussian noise image into the full-frequency fractional matching sub-model for image reconstruction.

[0048] Since the full-frequency fractional matching sub-model uses a stochastic differential equation with exploding variance during the training phase, the second step is specifically: using the obtained full-frequency continuous-time correlation fractional function To solve the inverse-time variance-exploding stochastic differential equation of the full-frequency fractional matching sub-model: , In the formula, Represents the full-frequency image in the wavelet domain during the image reconstruction phase Represents the full-frequency monotonically increasing function Is the uniform sampling time Represents the full-frequency logarithmic data distribution gradient Represents the inverse Brownian motion Represents the real number Represents the vector dimension.

[0049] The third step is to introduce the constraint of full-frequency prior information and at the same time use the fidelity term to enhance data consistency to obtain the th predicted image with discrete step length .

[0050] To ensure the reconstruction quality of complex objects behind the scattering medium, the constraint of full-frequency prior information is introduced to avoid large errors in the evolution of the stochastic differential equation with variance explosion in the discretization direction. Since the full-frequency fractional matching submodel uses the stochastic differential equation with variance explosion during the training phase, when solving the inverse-time stochastic differential equation with variance explosion, the constraint of full-frequency prior information is introduced to constrain the target image estimation process at each time step. The constraint of introducing full-frequency prior information in the third step is used to constrain the prediction process of the predictor (i.e., Figure 2 P in submodel 1 of , where, denotes the predicted image at the th discrete time step, is the factor balancing the data consistency term and the regularization term, denotes the fidelity term, denotes the wavelet transform, denotes the external index with the total number of time steps being , denotes the th discrete time step of the full-frequency image in the wavelet domain, denotes the th discrete time step of the noise intensity, denotes squared, denotes the th discrete time step of the noise intensity, denotes squared, is the function obtained by discretizing the full-frequency continuous-time correlation fractional function , is Gaussian noise.

[0051] In the fourth step, the annealed Langevin equation is used as the corrector (i.e., Figure 2 C in submodel 1 of ), and the fidelity term is used as the data consistency maintainer. The predicted image at the th discrete time step is input into the inner loop for correction to obtain the image to be reconstructed at the

[0052] th discrete time step. , where, denotes at As the full-frequency image in the wavelet domain at the th discrete step size under the internal loop input, represents the wavelet transform, represents the fidelity term, represents at As the full-frequency image in the wavelet domain at the th discrete step size under the internal loop input, is the internal index with a total step size of represents the th full-frequency step size at the th discrete step size, is the function obtained after discretizing the full-frequency continuous-time correlation fractional function is Gaussian noise.

[0053] After the inner loop ends, the th discrete step size of the image to be reconstructed is obtained .

[0054] In the fifth step, the th discrete step size of the image to be reconstructed is divided into the th discrete step size of the high-frequency component original image and the th discrete step size of the low-frequency component original image .

[0055] In the sixth step, the th discrete step size of the high-frequency component original image is input into the high-frequency fractional matching sub-model (i.e., the sub-model 2 in Figure 2 ), and is constrained by the high-frequency prior information. At the same time, the fidelity term is used as a data consistency maintainer for fidelity, so as to obtain the th discrete step size of the high-frequency component updated image .

[0056] Constraining the detail optimization process with high-frequency prior information, that is, using high-frequency prior information to constrain the solution of the stochastic differential equation with inverse-time variance explosion in the prediction correction stage, can comprehensively reconstruct the complex details and edge information of the image, while maintaining the basic characteristics of the reconstruction result. In the sixth step, when solving the stochastic differential equation with inverse-time variance explosion of the high-frequency fractional matching model using the obtained high-frequency continuous-time correlation fractional function , the high-frequency component original image is input into the high-frequency fractional matching sub-model (i.e., the sub-model 2 in Figure 2 ), and the predictor in the high-frequency fractional matching sub-model is respectively constrained by the high-frequency prior information (i.e.,Figure 2 in sub-model 2 of P) and the corrector (i.e., Figure 2 in sub-model 2 of C), and at the same time, using the fidelity term as a data consistency maintainer for fidelity, and its expression is as follows: , In the formula, represents the updated image of the high-frequency component in the wavelet domain at the th discrete step size, represents the updated image of the high-frequency component in the wavelet domain at the th discrete step size with as the input of the inner loop, , respectively represent the factors for balancing the data consistency term and the regularization term, represents the fidelity term the high-frequency image after wavelet transform , , , respectively represent the low-frequency-high-frequency subband image, high-frequency-low-frequency subband image, and high-frequency-high-frequency subband image obtained after the fidelity term undergoes wavelet transform, is the original high-frequency component image at the th discrete step size, represents the th discrete step size, represents the th discrete step size of the noise intensity, represents squared, represents the th discrete step size of the noise intensity, represents squared, represents the updated image of the high-frequency component in the wavelet domain at the th discrete step size with as the input of the inner loop.

[0057] Step 7: After weighted summation of the updated image of the high-frequency component at the th discrete step size [[ID=7H]] and the original high-frequency component image at the th discrete step size , combine and optimize it with the original low-frequency component image at the th discrete step size , perform inverse wavelet transform and total variation regularization term denoising on the optimized wavelet domain image to obtain the denoised spatial domain image.

[0058] In the seventh step, the optimized wavelet-domain image is subjected to inverse wavelet transform to obtain the spatial-domain image with the th discrete step size. And the total variation regularization term ( Figure 2 TV in ) is used to further denoise, and the spatial-domain image with the th discrete step size after denoising is expressed as follows: In the formula, represents the spatial-domain image with the th discrete step size after denoising, represents the inverse wavelet transform, represents the updated image of the high-frequency component in the wavelet domain with the th discrete step size, represents the original image of the high-frequency component with the th discrete step size, represents the original image of the low-frequency component with the th discrete step size, is the weight factor.

[0059] In the eighth step, the denoised spatial-domain image is used as the input again after wavelet processing. The loop is ended after repeating the second to seventh steps for a preset number of times, and the spatial-domain image output after the last loop is used as the reconstructed image similar to the target object . In the specific implementation process, for example, when the preset number of times is 1000, the eighth step outputs a reconstructed image with very few artifacts and high clarity.

[0060] To evaluate the performance of the scattering imaging image reconstruction method based on the wavelet-domain double fractional matching model in the present invention, 50 images are randomly selected from the preprocessed dataset as the test set. To simulate the actually captured speckle images, each image in the test set is convolved with the measured value of the point spread function to obtain the speckle pattern. The traditional deconvolution algorithm and the diffusion model algorithm are selected as the comparison algorithms, and the peak signal-to-noise ratio and the structural similarity are selected as the evaluation indexes. The comparison results are shown in Table 1.

[0061] Table 1 Comparison table of peak signal-to-noise ratio and structural similarity

[0062] The image reconstruction effect is as Figure 3 shown. Figure 3 (a) in Figure 3 are 6 real images, Figure 3Among them, (c), (d), and (e) are the reconstructed images output by the traditional deconvolution algorithm, the diffusion model algorithm, and the present invention respectively for each speckle image. To better show the quality of the reconstructed images, only the region of interest of 56×56 pixels is shown. From Figure 3 it can be seen that for complex objects, the reconstructed images output by the traditional deconvolution algorithm and the diffusion model algorithm both show obvious horizontal and vertical stripes. In contrast, the reconstructed image output by the present invention shows fewer artifacts and retains clearer details. The test results show that the quality of the reconstructed image of the present invention is better than the existing two methods.

[0063] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A scattering imaging image reconstruction method based on a wavelet domain double fractional matching model, characterized in that The method includes: In the prior information extraction stage, the trained full-frequency score matching sub-model and high-frequency score matching sub-model are used to extract the full-frequency and high-frequency prior information of the target object; In the image reconstruction stage, under the double constraints of the full-frequency and high-frequency prior information, the speckle image of the target object behind the scattering medium acquired by the image sensor is used as the fidelity term after Wiener deconvolution, support domain constraint, and bilateral filtering processing, and image reconstruction is performed. The reconstruction process includes: First, randomly generate four two-dimensional Gaussian noise images; Second, input the Gaussian noise image into the full-frequency score matching sub-model for image reconstruction; Third, introduce the constraint of the full-frequency prior information, and at the same time use the fidelity term to enhance data consistency to obtain a predicted image; Fourth, use the annealed Langevin equation as a corrector and the fidelity term as a data consistency maintainer, input the predicted image into the inner loop for correction to obtain the image to be reconstructed; Fifth, divide the image to be reconstructed into a high-frequency component original image and a low-frequency component original image; Sixth, input the high-frequency component original image into the high-frequency score matching sub-model, and use the high-frequency prior information for constraint, and at the same time use the fidelity term as a data consistency maintainer for fidelity to obtain a high-frequency component updated image; Seventh, after weighted summing the high-frequency component updated image and the high-frequency component original image, merge and optimize it with the low-frequency component original image, perform inverse wavelet transform and total variation regularization term denoising on the optimized wavelet domain image to obtain the denoised spatial domain image; Eighth, after wavelet processing the denoised spatial domain image and using it as the input again, repeat the second to seventh steps for a preset number of times to end the loop, and use the spatial domain image output after the last loop as the reconstructed image similar to the target object.

2. The method according to claim 1, characterized in that, Before the prior information extraction stage, there is also a model training stage, including: Using wavelet transform to convert the single-channel spatial domain image dataset of the target object into a four-channel full-frequency image dataset in the wavelet domain and a three-channel high-frequency image dataset in the wavelet domain; Using the two datasets obtained after wavelet transform to train the first original score matching model and the second original score matching model respectively to obtain the trained full-frequency score matching sub-model and high-frequency score matching sub-model.

3. The method according to claim 2, wherein For the full-frequency score matching sub-model, the obtaining process includes: Configure the stochastic differential equation with exploding variance used in the model training stage, and the expression is as follows: ， In the formula, represents the full-frequency image dataset in the four-channel wavelet domain, represents the full-frequency monotonically increasing function, represents the full-frequency diffusion coefficient, is the uniform sampling time, represents at Brownian motion in the dimensional real space, represents the vector dimension; Through training, use the full-frequency continuous-time correlation score function to estimate the gradient of the full-frequency log data distribution, and model this estimation process as solving the following full-frequency core objective function in the environment of the score-based stochastic differential equation: ， In the formula, represents the optimal parameters for the training of the full-frequency neural network, represents the training parameters of the full-frequency neural network, represents the expectation, represents the positive weight function, represents the training samples of the full-frequency image in the four-channel wavelet domain, is the full-frequency Gaussian perturbation kernel centered on, represents the full-frequency continuous-time correlation fractional function, is the full-frequency logarithmic data distribution gradient of.

4. The method according to claim 2, wherein For the high-frequency score matching sub-model, the obtaining process includes: Configure the stochastic differential equation with exploding variance used in the model training stage, and the expression is as follows: ， In the formula, represents the high-frequency image data set in the three-channel wavelet domain, represents the high-frequency monotonically increasing function, represents the high-frequency diffusion coefficient, is the uniform sampling time, represents at dimensional real space Brownian motion, represents a real number, represents the vector dimension; Through training, use the high-frequency continuous-time correlation score function to estimate the gradient of the high-frequency log data distribution, and model this estimation process as solving the following high-frequency core objective function in the environment of the score-based stochastic differential equation: ， In the formula, represents the optimal parameters for high-frequency neural network training, represents the training parameters of the high-frequency neural network, represents the expectation, represents the positive weight function, represents the training samples of the high-frequency image in the three-channel wavelet domain, is the high-frequency Gaussian perturbation kernel centered on, represents the high-frequency continuous-time correlation fractional function, is the high-frequency logarithmic data distribution gradient of.

5. The method according to claim 1, characterized in that After the speckle image undergoes Wiener deconvolution, support domain constraint, and bilateral filtering processing, it is used as the fidelity term, specifically including: After processing the speckle image using Wiener deconvolution, the deconvolved image is obtained, and its expression is as follows: ， In the formula, is the image after deconvolution, represents the Fourier transform, is the speckle image, is the point spread function in the Fourier domain, is the conjugate of, represents the adjustable parameter of the noise; The deconvolved image is subjected to support domain constraint and bilateral filtering to obtain the fidelity term, and the expression is as follows: ， In the formula, represents a pixel position on the image after deconvolution, represents another pixel position on the image after deconvolution, denotes the fidelity term at the pixel in it, represents the pixel value at the pixel in the image after deconvolution, represents the pixel value at the pixel in the image after deconvolution, is a normalization factor used to ensure that the sum of weights is 1, is the neighborhood of the pixel , is a Gaussian function in the spatial domain, is the standard deviation in the spatial domain, is a Gaussian function in the intensity domain, is the standard deviation in the intensity domain, is the region of interest in the actual imaging field.

6. The method according to claim 3, wherein The second step is specifically as follows: Using the obtained full-frequency continuous-time correlation fractional function Solve the stochastic differential equation of inverse time variance explosion of the full-frequency fractional matching sub-model: ， In the formula, represents the full-frequency image in the wavelet domain during the image reconstruction stage, represents the full-frequency monotonically increasing function, is the uniform sampling time, represents the full-frequency logarithmic data distribution gradient, represents the inverse Brownian motion, represents a real number, represents the vector dimension.

7. The method according to claim 6, wherein When solving the stochastic differential equation with inverse time variance explosion, the constraint of introducing full-frequency prior information in the third step is adopted, and at the same time, the fidelity term is used to enhance data consistency, and its expression is as follows: ， In the formula, represents the predicted image at the -th discrete step size, is the factor that balances the data consistency term and the regularization term, represents the fidelity term, represents the wavelet transform, represents the external index when the total time step is , represents the full-frequency image in the wavelet domain at the -th discrete step size, represents the noise intensity at the -th discrete step size, represents squared, represents the noise intensity at the -th discrete step size, represents squared, is the function obtained by discretizing the full-frequency continuous-time correlation fractional function , is Gaussian noise.

8. The method according to claim 7, wherein In the fourth step, the annealing Langevin equation is used as a corrector, the fidelity term is used as a data consistency maintainer, and the predicted image is input into the internal loop for correction, and its expression is as follows: ， In the formula, represents the full-frequency image in the wavelet domain at the th discrete step size under the internal loop input, represents the factor that balances the data consistency term and the regularization term, represents the wavelet transform, represents the fidelity term, represents the full-frequency image in the wavelet domain at the th discrete step size under the internal loop input, is the internal index with a total step size of , represents the full-frequency step size at the th discrete step size, is the function obtained by discretizing the full-frequency continuous-time correlation fractional function , is Gaussian noise.

9. The method according to claim 8, characterized in that, In the sixth step, when using the obtained high-frequency continuous-time correlation score function to solve the stochastic differential equation with inverse time variance explosion of the high-frequency fractional matching model, the original high-frequency component image is input into the high-frequency fractional matching sub-model, and is constrained by using high-frequency prior information, and at the same time, the fidelity term is used as a data consistency maintainer for fidelity, and its expression is as follows: ， In the formula, represents the updated image of the high-frequency component in the wavelet domain at the -th discrete step size, represents the updated image of the high-frequency component in the wavelet domain at the -th discrete step size with as the input of the inner loop, and respectively represent the factors for balancing the data consistency term and the regularization term, represents the fidelity term the high-frequency image after wavelet transform, , and and respectively represent the low-frequency - high-frequency subband image, high-frequency - low-frequency subband image, and high-frequency - high-frequency subband image obtained after wavelet transform of the fidelity term , is the original high-frequency component image at the -th discrete step size, represents the -th discrete step size, represents the noise intensity at the -th discrete step size, represents squared, represents the noise intensity at the -th discrete step size, represents squared, represents the updated image of the high-frequency component in the wavelet domain at the -th discrete step size with as the input of the inner loop.

10. The method according to claim 1, characterized in that, In the seventh step, after weighted summation of the high-frequency component updated image and the high-frequency component original image, it is merged and optimized with the low-frequency component original image, and the inverse wavelet transform and total variation regularization term denoising are performed on the optimized wavelet domain image, and the expression is as follows: ， In the formula, represents the spatial domain image of the th discrete step size after denoising, represents the inverse wavelet transform, represents the updated image of the high-frequency component in the wavelet domain of the th discrete step size, represents the original image of the high-frequency component of the th discrete step size, represents the original image of the low-frequency component of the th discrete step size, is the weight factor.

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