An encoding imaging reconstruction method based on a point spread function prior

Abstract

The application discloses a kind of based on point spread function prior encoding imaging reconstruction method, including two stages: (1) the inversion stage of trainable, by learning the prior parameter in the forward model of encoding system, the blurred encoding image measured is mapped to intermediate reconstruction space after wiener filtering, preliminary decoding is completed;(2) artifact correction stage, using the improved U-Net structure, introduce wavelet transform to complete multi-level frequency domain filtering, eliminate the residual artifacts of intermediate reconstruction image, improve visual perception quality.The application aims at the problem of long time consumption and low definition in image reconstruction in lensless encoding imaging, builds a lightweight deep learning convolutional neural network based on physical model, with less memory requirement and faster convergence speed, effectively reduces the time of network training and image reconstruction, and improves the reconstruction quality of encoding image.

Description

Technical Field

[0001] This invention belongs to the field of lensless coded imaging technology, specifically a coded imaging reconstruction method based on a priori point spread function. Background Technology

[0002] Lensless coded imaging technology uses a monolithic coded mask to replace the complex optical components in traditional cameras to encode scene light, such as diffractive optical elements and coded apertures. It then uses computational imaging technology to invert the optical imaging process and reconstruct the image of the target scene. This shifts the main burden of imaging from the front-end optical imaging equipment to the back-end computational reconstruction technology, avoiding the alignment, integration, and manufacturing problems of complex lens groups in traditional imaging systems. It significantly reduces system thickness, weight, and cost, providing a reasonable and feasible approach for lightweight imaging systems such as miniature cameras. This technology has significant applications in security, wearable devices, implantable devices, and IoT sensor networks.

[0003] The core idea of ​​image reconstruction methods based on coded mask imaging is to systematically control the light field using a designed mask, combined with an image reconstruction algorithm in the computational system, to invert a clear target scene from a blurred, unfocused pattern. Currently, most research on coded mask imaging technology focuses on the structure of the coded mask itself, its imaging model, and application scenarios. However, the refocused image obtained in the back-end scene reconstruction process suffers from artifacts and loss of detail. Therefore, it is necessary to conduct further research on coded mask imaging systems to explore their potential for high-quality back-end image reconstruction and improve the overall imaging performance of the system.

[0004] Currently, existing backend reconstruction algorithms can be divided into two categories: traditional iterative optimization algorithms and deep learning algorithms based on neural networks. Ashok Veeraraghavan's team proposed the FlatCam system, which uses an amplitude-modulated separable coded mask imaging system. Based on SVD, BM3D, and TV algorithms, it achieved 512×512 visible light image reconstruction, but the quality of the reconstructed image was poor and the reconstruction target was simple (1. Asif, MS, Ayremlou, A., Sankaranarayanan, A., Veeraraghavan, A., & Baraniuk, RG (2017). FlatCam: Thin, Lensless Cameras Using Coded Aperture and Computation. IEEE Transactions on Computational Imaging, 3(3), 384–397.). Jiachen Wu et al. used Fresnel zone aperture to encode incoherent light into the form of wavefront and used compressed sensing algorithm to effectively eliminate double image artifacts caused by sparsity in natural scenes. This method significantly improves the signal-to-noise ratio of single-lens images, promoting the development of a flat, reliable camera architecture that does not require strict calibration. However, the application of traditional algorithms is still limited by their slow reconstruction speed (2. Wu J, Zhang H, Zhang W, et al. Single-shot lensless imaging with fresnel zoneaperture and incoherent illumination[J]. Light: Science & Applications, 2020, 9(1):53.). Deep learning-based image reconstruction methods are becoming increasingly popular due to their excellent reconstruction results. However, compared with traditional iterative methods, deep learning-based methods are difficult to interpret and lack a structured approach to integrate the knowledge of the imaging system. Unfolding optimization represents a middle ground between classical and deep learning methods. In unfolding optimization, the fixed number of iterations of the classical algorithm is interpreted as a deep network, with each iteration being a layer in the network. KRISTINAMONAKHOVA et al. conducted research on the Alternating Direction Multiplier (ADMM) algorithm for lensless imaging. They proposed several network variations along the spectrum between classical and deep methods by changing the number of trainable parameters, including Le-ADMM, Le-ADMM*, and Le-ADMM-U.Networks trade off data fidelity and image perception quality, generating more visually appealing images at the cost of reduced data fidelity. However, this method has complex constraints and image details are obscured by artifacts (3. Kristina Monakhova, Joshua Yurtsever, Grace Kuo, Nick Antipa, Kyrollos Yanny, and Laura Waller, "Learned reconstructions for practical mask-based lensless imaging," Opt. Express 27, 28075-28090 (2019)). Summary of the Invention

[0005] The purpose of this invention is to provide a coding imaging reconstruction method based on point spread function prior, in order to solve the problems of slow reconstruction speed of traditional methods, low reconstruction accuracy and artifact residue of deep learning methods in lensless coding imaging. With less memory requirements and faster convergence speed, it effectively reduces the time of network training and image reconstruction, while improving the reconstruction quality of coded images.

[0006] The technical solution to achieve the objective of this invention is: a coded imaging reconstruction method based on point spread function prior, the specific steps of which are as follows:

[0007] Step 1: Simulate or collect a set of lossless target datasets as reference images;

[0008] Step 2: Simulate or acquire a set of coded image datasets based on a lensless coded imaging system, generate training data pairs of a specified size, and calculate the point spread function of the coded mask of the corresponding size;

[0009] Step 3: Construct a reconstruction network. The reconstruction network adopts a convolutional neural network based on the point spread function prior. The reconstruction network consists of two parts: a Wiener filter inversion part based on the point spread function prior and an artifact correction part based on the wavelet convolutional neural network. A point spread function of a specified size is used as learnable prior information and input into the filter kernel of the Wiener filter inversion part.

[0010] Step 4: Construct the loss function of the reconstruction network: The error between the network output and the target image is calculated using the negative Pearson correlation coefficient. The loss function is defined as the quotient of the product of the covariance between the two variables and the standard deviation of each variable.

[0011] Step 5: Optimize the wavelet convolutional neural network using the Adam optimizer. Set the initial learning rate of the optimization algorithm, multiply it by the decay factor after each training cycle, and set the exponential decay rate of the first moment estimate, the exponential decay rate of the second moment estimate, and the number of iterations per cycle.

[0012] Step 6: Train the network according to the set hyperparameters, for a total of b cycles, in two steps: For the first b / 2 cycles, fix the Wiener filter kernel, meaning the Wiener filter inversion part does not participate in backpropagation, and only train the wavelet convolutional neural network module; after the first b / 2 cycles of training are completed, the network reaches a preliminary convergence state, and then perform the next b / 2 cycles of training. In the next b / 2 cycles of iteration, the Wiener filter module is included in the backpropagation process, that is, the parameters of both modules are trained simultaneously, where b is an even number;

[0013] Step 7: Input the encoded images of the test set into the network for prediction and output the reconstructed decoded images.

[0014] Compared with the prior art, the present invention has the following significant advantages: (1) It adopts the Wiener filtering fast reconstruction method based on the least squares problem under Tikhonov regularization to realize the initial decoding of the encoded image, makes full use of the prior physical information, establishes the inversion physical model, and incorporates the physical model into the deep learning network learning architecture, so that the reconstruction process is interpretable; (2) For the intermediate reconstructed image of the initial decoding, wavelet transform is introduced to replace each pooling operation, which expands the receptive field without losing information; (3) The network of the present invention only includes 32 convolutional layers, which greatly reduces the number of network parameters, improves the running speed, removes image artifacts, preserves image details, and improves reconstruction quality. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of a system model used to verify the present invention.

[0016] Figure 2 This is a schematic diagram of the light modulation process of the coding mask in this invention.

[0017] Figure 3 This is a schematic diagram of the wavelet convolutional neural network structure in this invention.

[0018] Figure 4 This is a schematic diagram of the overall structure of the method of the present invention.

[0019] Figure 5 These are comparison images of the image reconstructed by the coded imaging reconstruction method based on the point spread function prior of this invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings.

[0021] A coding imaging reconstruction method based on point spread function priors, the specific steps of which are as follows:

[0022] Step 1: Collect a set of lossless target datasets as reference images. You can use publicly available high-resolution datasets online or collect them yourself.

[0023] Step 2: Establish a lensless coded imaging system. For example... Figure 1 The diagram shown is a schematic of the system model used to verify the present invention. The target scene is a lossless image displayed on a screen. The screen is about 30 cm away from the coded mask, and the coded mask is about 3 mm away from the sensor. The coded mask replaces the traditional lens group and sensor module to form a lensless camera system. The verification system in this invention uses a Fresnel zone plate as a reference coded mask. The zone plate has a diameter of about 4.5 mm and a Fresnel constant of 0.325 mm.

[0024] A set of coded image datasets is simulated or acquired using a lensless coded imaging system. Training data pairs of a specified size are generated, and the point spread function of a coded mask of corresponding size is measured. For directly acquired datasets, a lensless coded imaging system is used to capture non-destructive images on a display screen under the above parameter conditions. For simulated datasets, a rigorous forward propagation model needs to be established to simulate the coded images captured on the sensor. The specific simulation process is described below.

[0025] The principle of lensless coded imaging is as follows: In Fourier optics, the formation of an incoherent image can be considered as a collection of point sources. Each point source will produce a shift effect on the point spread function. Since the sources are incoherent, the shifted point spread function will linearly increase in intensity at the sensor. The detected image can be represented as a convolution model of the target image and the system's point spread function. In this invention, the modulation effect of the coded mask on the incident light is expressed in the form of a point spread function, such as... Figure 2 As shown, the point spread function intensity map changes with the diffraction distance.

[0026] For sensor imaging, the process of generating the simulated coded image dataset is as follows:

[0027] Y = C(PSF) z *X+N)

[0028] Where Y is the coded image on the analog image plane, C is the cropping operator, and PSF is the PSF. zLet be the point spread function of the coded mask captured on the outgoing light field at a distance z from the target, X be the input lossless target image, N be additive noise, and * denote the convolution operator. For a broadband light source, the coded image can be calculated by integrating the diffraction intensities over multiple wavelengths. For a specific sensor, the imaging model also needs to consider a specific spectral response curve. This is because image sensors have different sensitivities to different wavelengths of light; therefore, the integration should be performed using the spectral responsivity Q. c (λ) weighting:

[0029]

[0030] Where, [λ min ,λ max ] indicates the spectral range, PSF z X(λ) is the point spread function for monochromatic light with wavelength λ, X(λ) is the intensity of light with wavelength λ emitted from the screen, and Q is the point spread function for monochromatic light with wavelength λ. c This is the spectral response curve of the sensor, and η is the readout noise of the sensor, typically Gaussian noise η~N(0,σ) 2 ),Y c It is an coded image captured by an analog sensor.

[0031] Step 3: Construct a reconstruction network. The reconstruction network adopts a convolutional neural network based on the point spread function prior. The reconstruction network consists of two parts: a Wiener filter inversion part based on the point spread function prior and an artifact correction part based on the wavelet convolutional neural network.

[0032] (1) The specific method for the Wiener filter inversion part is as follows:

[0033] Imaging models for lensless imaging systems based on masks are typically characterized by the convolution of the scene and the mask shadow, i.e., the point spread function (PSF):

[0034] y = p*x + e

[0035] In the formula, p is the point spread function, x is the scene irradiance, y is the image formed on the sensor, and e is the measurement noise. To reconstruct x from y using the known p, the general image restoration method for lensless imaging is to minimize the objective function, which is usually composed of data fidelity terms and regularization terms:

[0036]

[0037] in Quantify data fidelity, regularization terms Prior knowledge is introduced to mitigate the ill-posedness of the inverse problem, and the regularization parameter γ controls the relative weights of the two terms. Let Tikhonov regularization be used. The least squares problem under this Tikhonov regularization has a closed-form solution given by Wiener deconvolution:

[0038]

[0039] In the case of convolution, the form of the trainable inversion stage is represented in the Fourier domain as the learning inversion of the Hadamard product:

[0040] X interm =F -1 (F(W)⊙F(Y))

[0041] Among them, X interm This is the output of this stage, Y is the measurement result, and F(·) and F0 are the values ​​of F0 and F0. -1 (·) represents the Fourier transform and inverse Fourier transform operations, W is the filter learned by the neural network, and ⊙ refers to the Hadamard product. For a measurement with dimension N×M, the dimension of W is also N×M. W is initialized using the Fourier transform of the calibrated point spread function, i.e.:

[0042]

[0043] Where K is a regularization parameter, initially set to 10. 4 H = F(p), where p is the prior point spread function of the input. * Represents the conjugate operator.

[0044] In the reconstructed network, a point spread function of a specified size is input as learnable prior information into the filter kernel of the Wiener filter module.

[0045] (2) The wavelet convolutional neural network adopts the U-Net architecture, consisting of 4 layers of wavelet transform, 32 convolutional blocks, and 4 layers of inverse wavelet transform. Each convolutional block includes optional Batch Normalization (BN) and ReLU activation processes. Since the wavelet transform is reversible, this downsampling scheme ensures that all information is preserved. Furthermore, the wavelet transform can simultaneously capture the frequency and location information of the feature map, exhibiting good time-frequency localization characteristics and detail preservation capabilities. The wavelet transform enhances the network's learning of high-frequency and low-frequency information, which is beneficial for artifact correction. This wavelet convolutional neural network can embed the wavelet transform into any convolutional neural network with pooling and has a stronger ability to model spatial context and inter-subband dependencies.

[0046] Specifically, the wavelet convolutional neural network consists of two parts: an encoder subnetwork and a decoder subnetwork, both with a symmetrical U-shaped structure. In the encoder subnetwork, feature map downsampling is performed through wavelet transform layers, and four convolutional blocks are added between any two wavelet transform layers. The output subband feature map of the wavelet transform serves as the input to the subsequent convolutional blocks. Similarly, in the decoder subnetwork, feature map upsampling is performed through inverse wavelet transform, and four convolutional blocks are added between any two inverse wavelet transform layers. The output subband feature map of the inverse wavelet transform serves as the input to the subsequent convolutional layers. Each convolutional block consists of a 3×3 filter convolution, batch normalization, and a corrected linear unit (ReLU activation function). For the last convolutional block, a convolution without batch normalization and ReLU activation function is used to predict the residual image. During the upsampling process, the feature maps of the encoder and decoder subnetworks are fused using an element-wise summation method.

[0047] The wavelet transform is implemented as follows:

[0048] Taking the Haar wavelet as an example, in the two-dimensional Haar wavelet, the low-pass filter is defined as:

[0049]

[0050] It can be seen that, In practice, this implements a summation pooling operation. When only low-frequency subbands are considered, wavelet transform and inverse wavelet transform function as pooling and up-convolution, respectively, in the network. When all subbands are considered, the network avoids information loss caused by conventional subband sampling, which is beneficial for restoring the results. In the reconstruction network, f is also used... LH ,f HL ,f HH The three sub-band filters are defined as follows:

[0051]

[0052] Given an image x of size m×n, find the (i,j)th value x of the four sub-band images of the image after a 2D Haar transform (wavelet transform). k (i,j)(k=1,2,3,4) are written as follows:

[0053]

[0054] Meanwhile, the inverse wavelet transform process can be obtained as follows:

[0055]

[0056] The image size used for training is N×N×1. The output inversion image size after the input image passes through the Wiener filter module is also N×N×1. The wavelet convolutional neural network performs a total of 4 layers of downsampling feature learning operations and 4 layers of upsampling feature learning operations on the intermediate reconstructed image. The specific structure of the encoder subnetwork is as follows:

[0057] First feature layer: The input feature map is downsampled by the first wavelet transform, and the number of output channels is 4. Then, it is processed by 4 convolutional blocks to complete feature learning. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, a number of output channels of 40, a stride of 1, and padding of 1; (2) a batch normalization layer with a number of output channels of 40; (3) an activation layer, which is activated using the ReLU function; where the first convolutional layer has 4 input channels, and the second to fourth convolutional layers have 40 input channels.

[0058] Second feature layer: The output of the first feature layer is downsampled by the second wavelet transform, with 160 output channels, and then features are learned by four convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 64 output channels; and (3) an activation layer activated by the ReLU function. The first convolutional layer has 160 input channels, and the second to fourth convolutional layers have 64 input channels.

[0059] The third feature layer: The output of the second feature layer is downsampled by the third wavelet transform, with 256 output channels, and then features are learned by four convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 64 output channels; and (3) an activation layer activated by the ReLU function. The first convolutional layer has 256 input channels, and the second to fourth convolutional layers have 64 input channels.

[0060] Fourth Feature Layer: The output of the third feature layer is downsampled by the fourth wavelet transform, with 256 output channels. Then, it is processed by four convolutional blocks to complete feature learning. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 64 output channels; and (3) an activation layer activated using the ReLU function. The first convolutional layer has 256 input channels, and the second to fourth convolutional layers have 64 input channels.

[0061] The specific structure of the decoder subnetwork is as follows:

[0062] Fourth Feature Layer: The output of the fourth feature layer of the encoder is used as input. First, it goes through 4 convolutional blocks to complete feature learning. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, a number of 64 kernels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, which is activated using the ReLU function. The first to third convolutional layers and the batch normalization layer have 64 output channels, and the fourth convolutional layer and the batch normalization layer have 256 output channels. Then, the fourth layer performs inverse wavelet transform to complete upsampling, and the number of output channels is 64.

[0063] The third feature layer: The output of the encoder's third feature layer is added to the output of the decoder's fourth feature layer and used as the input of the decoder's third feature layer. First, feature learning is completed through 4 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 input channels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, activated using the ReLU function; where the first to third convolutional layers and the batch normalization layer have 64 output channels, and the fourth convolutional layer and the batch normalization layer have 256 output channels; then, upsampling is completed through the third layer wavelet inverse transform, with 64 output channels.

[0064] Second feature layer: The output of the second feature layer of the encoder is added to the output of the third feature layer of the decoder and used as the input of the second feature layer of the decoder. First, feature learning is completed through 4 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 input channels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, activated using the ReLU function; where the output channels of the first to third convolutional layers and the batch normalization layer are 64, and the output channels of the fourth convolutional layer and the batch normalization layer are 160; then, upsampling is completed through two layers of wavelet inverse transform, and the output channels are 40.

[0065] First feature layer: The output of the encoder's first feature layer is added to the output of the decoder's second feature layer and used as the input of the decoder's first feature layer. First, feature learning is completed through 3 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 40 input channels, 40 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 40 output channels; (3) an activation layer activated using the ReLU function; then through a fourth convolutional layer with a kernel size of 3×3, 40 input channels, 4 output channels, a stride of 1, and padding of 1; finally, upsampling is completed through the first layer of wavelet inverse transform, with 1 output channel.

[0066] Zero Feature Layer: The encoder input is added to the output of the decoder's first feature layer to obtain the final output.

[0067] Step 4: Construct the loss function for the reconstruction network: Let X be the input encoded image of the network, Y be the corresponding lossless target image, and T be the output reconstructed image. The negative Pearson correlation coefficient is used to calculate the error between the network output and the target image. This loss function is defined as the quotient of the product of the covariance between the two variables and the standard deviation of each variable.

[0068]

[0069] Where n is the number of pixels in the input image, and i iterates through the grayscale value corresponding to each pixel. The range of this loss function is [-1, 0], and the closer it is to -1, the higher the correlation and the better the image reconstruction effect.

[0070] Step 5: The entire network is optimized using the Adam (Adaptive Moment Estimate) optimizer. The initial learning rate (lr) of this optimization algorithm is set to 0.0005. After each training cycle, the learning rate is multiplied by a decay factor of 0.8. The exponential decay rate of the first moment estimate is 0.9, and the exponential decay rate of the second moment estimate is 0.999. 3200 pairs of samples are created, the batch processing number of images is 4, and a total of 800 iterations are completed in each cycle.

[0071] Step 6: As Figure 4 The diagram shows the overall structure of the method of the present invention. Based on this diagram, the network is trained according to the set hyperparameters for a total of 40 cycles, which are completed in two stages: the Wiener filter kernel is fixed for the first 20 cycles, that is, the Wiener filter module does not participate in backpropagation, and only the wavelet convolutional neural network module is trained; after the 20 cycles of training are completed, the network reaches a preliminary convergence state, and then the next 20 cycles of training are performed. In this iteration, the Wiener filter module is included in the backpropagation process, that is, the parameters of the two modules are trained simultaneously.

[0072] Step 7: Save the final trained network model, input the encoded images of the test set into the network for prediction, and output the reconstructed decoded images.

[0073] Figure 5 This is a comparison of the image quality reconstructed by the coded imaging reconstruction method based on the point spread function prior of this invention. On the test set, the average reconstruction time for a 1024×1024 image using this method is 0.033s, and the average peak signal-to-noise ratio is 22.15dB.

Claims

1. A coding imaging reconstruction method based on point spread function prior, characterized in that, The specific steps are as follows: Step 1: Simulate or collect a set of lossless target datasets as reference images; Step 2: Simulate or acquire a set of coded image datasets based on a lensless coded imaging system, generate training data pairs of a specified size, and calculate the point spread function of the coded mask of the corresponding size; Step 3: Construct a reconstruction network. The reconstruction network adopts a convolutional neural network based on the point spread function prior. The reconstruction network consists of two parts: a Wiener filter inversion part based on the point spread function prior and an artifact correction part based on the wavelet convolutional neural network. A point spread function of a specified size is used as learnable prior information and input into the filter kernel of the Wiener filter inversion part. Step 4: Construct the loss function of the reconstruction network: The error between the output of the reconstruction network and the reference image is calculated using the negative Pearson correlation coefficient. The loss function is defined as the quotient of the product of the covariance between the two variables and the standard deviation of each variable. Step 5: Optimize the wavelet convolutional neural network using the Adam optimizer. Set the initial learning rate of the optimization algorithm, multiply it by the decay factor after each training cycle, and set the exponential decay rate of the first moment estimate, the exponential decay rate of the second moment estimate, and the number of iterations per cycle. Step 6: Train the reconstruction network according to the set hyperparameters, for a total of b cycles, in two steps: For the first b / 2 cycles, fix the Wiener filter kernel, that is, the Wiener filter inversion part does not participate in backpropagation, and only the wavelet convolutional neural network part is trained; after the first b / 2 cycles of training are completed, the network reaches the initial convergence state, and then the next b / 2 cycles of training are performed. In the next b / 2 cycle iteration, the Wiener filter part is included in the backpropagation process, that is, the parameters of both parts are trained simultaneously, where b is an even number; Step 7: Input the encoded images of the test set into the network for prediction and output the reconstructed decoded images.

2. The coded imaging reconstruction method based on point spread function prior as described in claim 1, characterized in that: The lensless coded imaging system includes a display screen, a coded mask, and an image acquisition device arranged on the same horizontal optical path. The display screen shows a non-destructive target scene, the display screen is about 30cm away from the coded mask, and the coded mask is 3mm away from the image acquisition device.

3. The coded imaging reconstruction method based on point spread function prior as described in claim 1, characterized in that: The process of generating the simulated encoded image dataset in step 2 is as follows: in, It is a coded image on a simulated image plane. It is a cutting operator. It is the point spread function of the encoded mask captured on the emitted light field at a distance z from the target. It is the input lossless target image. Additive noise, This represents the convolution operator.

4. The coded imaging reconstruction method based on point spread function prior as described in claim 1, characterized in that, The specific process of the Wiener filter inversion part based on the point spread function prior in step 3 is as follows: in, This is the output of the Wiener filter inversion part. It is a measurement result. and These are the Fourier transform and inverse Fourier transform operations, respectively. It is a filter learned by a neural network, and Refers to the Hadamard product; for a given dimension, it is The measured value, The dimension is also ; Initialization is performed using the Fourier transform of the calibrated point spread function, i.e.: Where K is a regularization parameter. , The point spread function is the prior for the input. Represents the conjugate operator.

5. The coded imaging reconstruction method based on point spread function prior as described in claim 1, characterized in that, The wavelet convolutional neural network part in step 3 consists of two parts: an encoder and a decoder, both of which have a symmetrical U-shaped structure.

6. The coded imaging reconstruction method based on point spread function prior as described in claim 5, characterized in that, The encoder includes four wavelet transform layers, each followed by four convolutional blocks. The wavelet transform layers perform feature map downsampling. Each convolutional block consists of a 3 × 3 filter convolution, batch normalization, and a corrected linear unit.

7. The coded imaging reconstruction method based on point spread function prior as described in claim 6, characterized in that, The encoder includes: First feature layer: The input feature map is downsampled by the first wavelet transform and then processed by 4 convolutional blocks to complete feature learning. After downsampling, the number of output channels is 4. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 40 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 40 output channels; (3) an activation layer activated by the ReLU function. The first convolutional layer has 4 input channels, and the second to fourth convolutional layers have 40 input channels. Second feature layer: The output of the first feature layer is downsampled by the second wavelet transform and then feature learning is completed by 4 convolutional blocks. After downsampling, the number of output channels is 160. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 64 output channels; (3) an activation layer activated by the ReLU function. The first convolutional layer has 160 input channels, and the second to fourth convolutional layers have 64 input channels. The third feature layer: The output of the second feature layer is downsampled by the wavelet transform of the third layer, and the feature learning is completed by 4 convolutional blocks. After downsampling, the number of output channels is 256. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, an output channel of 64, a stride of 1, and padding of 1; (2) a batch normalization layer with an output channel of 64; (3) an activation layer using the ReLU function for activation; where the first convolutional layer has an input channel of 256, and the second to fourth convolutional layers have an input channel of 64. Fourth feature layer: The output of the third feature layer is downsampled by the fourth wavelet transform and feature learning is completed by 4 convolutional blocks. After downsampling, the number of output channels is 256. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, an output channel of 64, a stride of 1, and padding of 1; (2) a batch normalization layer with an output channel of 64; (3) an activation layer activated by the ReLU function. The first convolutional layer has an input channel of 256, and the second to fourth convolutional layers have an input channel of 64.

8. The coded imaging reconstruction method based on point spread function prior as described in claim 6, characterized in that, The decoder includes four inverse wavelet transform layers, each followed by four convolutional blocks. For the last convolutional block, convolution without batch normalization and ReLU activation is used to predict the residual image. The inverse wavelet transform layers are used to perform feature map upsampling. During the upsampling process, the feature maps of the encoder and decoder are fused using an element-wise summation method.

9. The coded imaging reconstruction method based on point spread function prior as described in claim 6, characterized in that, The decoder includes: Fourth Feature Layer: The output of the fourth feature layer of the encoder is used as input and is processed through 4 convolutional blocks to complete feature learning. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, a number of 64 kernels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, activated using the ReLU function; where the first to third convolutional layers and the batch normalization layer have 64 output channels, and the fourth convolutional layer and the batch normalization layer have 256 output channels; after upsampling is completed by the fourth wavelet inverse transform, the number of output channels is 64. The third feature layer: The output of the encoder's third feature layer is added to the output of the decoder's fourth feature layer and used as the input of the decoder's third feature layer. Feature learning is completed through 4 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 input channels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, activated using the ReLU function; where the first to third convolutional layers and the batch normalization layer have 64 output channels, and the fourth convolutional layer and the batch normalization layer have 256 output channels; after upsampling is completed by the third wavelet inverse transform, the number of output channels is 64. Second feature layer: The output of the second feature layer of the encoder is added to the output of the third feature layer of the decoder and used as the input of the second feature layer of the decoder. First, feature learning is completed through 4 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 64 input channels, a stride of 1, and padding of 1; (2) a batch normalization layer; (3) an activation layer, activated using the ReLU function; where the output channels of the first to third convolutional layers and the batch normalization layer are 64, and the output channels of the fourth convolutional layer and the batch normalization layer are 160; then, upsampling is completed through two layers of wavelet inverse transform, and the output channels are 40. First feature layer: The output of the encoder's first feature layer is added to the output of the decoder's second feature layer and used as the input of the decoder's first feature layer. First, feature learning is completed through 3 convolutional blocks. Each convolutional block includes: (1) a convolutional layer with a kernel size of 3×3, 40 input channels, 40 output channels, a stride of 1, and padding of 1; (2) a batch normalization layer with 40 output channels; (3) an activation layer activated using the ReLU function; then through a fourth convolutional layer with a kernel size of 3×3, 40 input channels, 4 output channels, a stride of 1, and padding of 1; finally, upsampling is completed through the first layer of wavelet inverse transform, with 1 output channel. Zero Feature Layer: The encoder input is added to the output of the decoder's first feature layer to obtain the final output.

10. The coded imaging reconstruction method based on point spread function prior according to claim 1, characterized in that, The loss function constructed in step 4 is as follows: in, The input image should have a pixel count. Iterate through each pixel. To reconstruct the pixels in the image The corresponding grayscale value, The table shows the mean grayscale values ​​of all pixels in the reconstructed image. For pixels in the lossless target image The corresponding grayscale value, This is the average grayscale value of all pixels in the lossless target image.

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