A method for imaging restoration of sparse aperture systems

Abstract

The present invention discloses a method for restoring sparse aperture system imaging, comprising the following steps: establishing a database of sparse aperture system imaging and corresponding optical transfer functions; constructing a deep neural network, including determining the network structure, activation function, and loss function; training the convolutional neural network using a training set; and realizing sparse aperture imaging restoration based on the optical transfer function. The present invention uses a deep convolutional neural network to obtain an unknown optical transfer function, which has a simple principle and is easy to implement; the present invention uses a deep convolutional neural network to restore clear imaging of a sparse aperture optical system through a computer program, without the need for expensive optical equipment and at a low cost; the present invention uses two convolutional neural networks to respectively calculate the modulation transfer function and the phase transfer function, which can be calculated in parallel and has a fast calculation speed.

Description

Technical Field

[0001] The invention belongs to the technical field of image processing, and relates to a method for realizing sparse aperture system imaging restoration by using a digital image processing method. Background Art

[0002] The sparse aperture system uses multiple small sub-apertures to replace the equivalent large aperture optical system to solve the problems of difficult processing, large emission volume and heavy weight of large aperture optical systems. However, due to the small light-transmitting area of ​​the sparse aperture imaging system, the imaging contrast and image quality are reduced. To this end, Chen Hao of Zhejiang University proposed an improved Wiener filter algorithm in the paper "Research on Image Restoration Algorithm of Optical Sparse Aperture Imaging System", which does not require prior information to obtain suitable restoration results. Zhou Chenghao of Harbin Institute of Technology used a spatially varying image restoration algorithm and image fusion method in the paper "Research on Design of Optical Sparse Aperture System and Method for Improving Intermediate Frequency Information", and improved the imaging performance of the optical sparse aperture imaging system by enhancing and compensating the intermediate frequency information of two types of systems with large filling factors and small filling factors. There may be installation errors in the multiple sub-apertures of the sparse aperture system, and the optical surfaces may be deformed and displaced, causing the sub-apertures to be out of "phase", seriously reducing the imaging quality of the optical system.

[0003] Liu Zheng and others from the National University of Defense Technology theoretically analyzed the impact of phase shift errors and sub-aperture aberrations on the system's image quality. Zhou Zhiwei from Beijing University of Technology discussed the stability of the image restoration algorithm when the system is subject to phase error in "Research on Phase Error and Image Restoration of Optical Sparse Aperture Imaging Systems". However, neither of them has yet provided a solution for image restoration. Liu Zheng and others from the Institute of Optoelectronics Technology of the Chinese Academy of Sciences proposed a phase shift error correction device for a sparse optical synthetic aperture imaging system to detect and compensate for the system's phase shift error. However, for sparse aperture systems operating in orbit, it is very difficult to build such a device, and the correction method is difficult to implement. Summary of the invention

[0004] The purpose of the present invention is to propose a sparse aperture system imaging restoration method in view of the shortcomings of the prior art, to make up for the defects of image quality degradation and difficulty in imaging restoration caused by assembly errors, deformations, displacements, etc. of various components of the sparse aperture system, and to improve the applicability of the sparse aperture system.

[0005] The technical solution of the present invention is:

[0006] A sparse aperture system imaging restoration method comprises the following steps:

[0007] Step 1: Establish a database of sparse aperture system imaging and corresponding optical transfer functions;

[0008] Step 2: Build a deep neural network, including determining the network structure, activation function, and loss function;

[0009] Step 3: Use the training set to train the convolutional neural network;

[0010] Step 4: Realize sparse aperture imaging restoration based on optical transfer function.

[0011] Furthermore, in step 1, the optical design software ZEMAX is used to establish a sparse aperture system simulation system. The software is used to simulate various tilt, displacement, and curvature radius change conditions of the optical surface, and the point spread function under each condition is obtained by the software, and the modulation transfer function and phase transfer function are further calculated.

[0012] Furthermore, the step 1 comprises:

[0013] Step 1-1: Simulate the sparse aperture optical system. According to the component parameters of the sparse aperture optical system, establish a simulation system in ZEMAX software;

[0014] Step 1-2: Set the error range of optical surface parameters. Usually, the tilt, displacement, and curvature radius of the optical surface change very small. The tilt will rotate around the x, y, and z axes passing through the vertex of the optical surface. The rotation angle range is [-0.01°, 0.01°], and the values ​​are taken at equal intervals of 0.005° as the step size. There are 5 values ​​in total, and a total of 125 values ​​for the three axes. The displacement range along the x, y, and z directions is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ as the step size. λ is the wavelength. There are 11 values ​​in total, and a total of 1331 values ​​for the three axes. The curvature radius change range is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ as the step size. λ is the wavelength. There are 11 values ​​in total, so there are about 1830125 errors for an optical surface. For the golay3 system, there are three sub-mirrors, so there may be 6.1×10 18 kind of error;

[0015] Step 1-3: Use ZEMAX software to extend the programming method, simulate various optical surface errors within the error range of step 2, and output the corresponding modulation transfer function and phase transfer function. For the selected target, obtain the corresponding sparse aperture system imaging under various error conditions. Thus, the corresponding relationship between sparse aperture system imaging and modulation transfer function and phase transfer function is established.

[0016] Furthermore, the step 2 includes: converting the pixel value of the input sparse aperture image into a number between 0 and 1, calculating the amplitude of its Fourier transform to obtain its amplitude as the input of the amplitude deep neural network; calculating its phase angle as the input of the phase deep neural network.

[0017] Furthermore, the step 3 includes: for the training set data, setting the initial value, the learning rate, and formulating a learning rate change strategy, and inputting the target image into the neural network to carry out network training.

[0018] Furthermore, step 4 includes: normalizing the pixel values ​​of the image obtained by imaging the sparse aperture system to a number between 0 and 1. After the image is Fourier transformed, its modulus and phase angle are taken, and after normalization, they are respectively input into the corresponding neural network, and their respective transfer functions are calculated and merged into an optical transfer function. After the image obtained by imaging the sparse aperture system is Fourier transformed, the optical transfer function is used to perform image restoration processing, and the result is inverse Fourier transformed to obtain the imaging restoration result.

[0019] Compared with the prior art, the present invention has the following characteristics:

[0020] (1) The present invention uses a deep convolutional neural network to obtain the unknown optical transfer function, which has a simple principle and is easy to implement.

[0021] (2) The present invention uses a deep convolutional neural network to restore clear imaging of a sparse aperture optical system through a computer program, without the need for expensive optical equipment and at a low cost.

[0022] (3) The present invention uses two convolutional neural networks to calculate the modulation transfer function and the phase transfer function respectively, which can be calculated in parallel and has a fast calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart for establishing sparse aperture system imaging and corresponding optical transfer function database.

[0024] Figure 2 It is a diagram of the deep neural network structure.

[0025] Figure 3 It is a flowchart of the imaging restoration process.

[0026] Figure 4 This is a Golay3 structure sparse aperture optical system according to embodiment 1.

[0027] Figure 5 It is the object plane diagram used in the first embodiment.

[0028] Figure 6 This is the Golay3 structure sparse aperture system imaging obtained by simulation in Example 1.

[0029] Figure 7 This is a false color diagram of the modulation transfer function of the Golay3 structure sparse aperture system in Example 1.

[0030] Figure 8 It is a phase transfer function diagram of the Golay3 structure sparse aperture system in Example 1.

[0031] Fig. 9 It is the object plane diagram used in the second embodiment.

[0032] Fig.10 It is a modulation transfer function diagram obtained by simulation when there is a tilt error in the sub-mirror 1 in the second embodiment.

[0033] Fig.11 It is a phase transfer function diagram obtained by simulation when there is a tilt error in sub-mirror 1 in Example 2.

[0034] Fig.12 This is the Golay3 multi-mirror telescope system imaging obtained by simulation when there is a tilt error in sub-mirror 1 in Example 2.

[0035] Fig.13 It is a modulation transfer function diagram obtained by simulation when there is a tilt error in the sub-mirror 2 in the second embodiment.

[0036] Fig.14 It is a phase transfer function diagram obtained by simulation when there is a tilt error in the sub-mirror 2 in the second embodiment.

[0037] Fig.15 This is the Golay 3 multi-mirror telescope system imaging obtained by simulation when there is a tilt error in sub-mirror 2 in Example 2.

[0038] Fig.16 It is a modulation transfer function diagram obtained by simulation when there is a displacement error in sub-mirror 1 in embodiment 2.

[0039] Fig.17 It is a phase transfer function diagram obtained by simulation when there is a displacement error in sub-mirror 1 in Example 2.

[0040] Fig.18 This is the Golay 3 multi-mirror telescope system imaging obtained by simulation when there is a displacement error in sub-mirror 1 in Example 2.

[0041] Fig.19 It is a modulation transfer function diagram obtained by simulation when there is a displacement error in the sub-mirror 2 in the second embodiment.

[0042] Fig. 20 It is a phase transfer function diagram obtained by simulation when there is a displacement error in the sub-mirror 2 in the second embodiment.

[0043] Fig.21 This is the Golay 3 multi-mirror telescope system imaging obtained by simulation when there is a displacement error in sub-mirror 2 in Example 2.

[0044] Fig. 22 This is the Golay3 structure sparse aperture system imaging obtained by simulation when there is a tilt error in sub-mirror 1 in Example 3.

[0045] Fig.23 This is the object plane result obtained by restoring the optical transfer function without error in the third embodiment.

[0046] Fig.24 This is a modulation transfer function diagram obtained by calculating the deep neural network of the present invention when there is a tilt error in the sub-mirror 1 in Example 3.

[0047] Fig.25 This is a phase transfer function diagram obtained by calculating the deep neural network of the present invention when there is a tilt error in the sub-mirror 1 in Example 3.

[0048] Fig.26 This is the object plane result obtained by estimating the optical transfer function and restoring the object plane using the method of the present invention in Example 3. DETAILED DESCRIPTION

[0049] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0050] The present invention provides a sparse aperture system imaging restoration method. In the case of errors in the sparse aperture system components, a convolutional neural network model is constructed to establish a mapping relationship between fuzzy imaging and the system optical transfer function, so that the convolutional neural network has the ability to estimate the system optical transfer function from the fuzzy imaging. The optical transfer function corresponding to the fuzzy imaging is obtained by using the trained convolutional neural network, and then the sparse aperture system imaging restoration is realized by Wiener filtering.

[0051] The imaging process of a sparse aperture optical system can be expressed as

[0052] g(x,y)=f(x,y)*h(x,y)+n(x,y) (1)

[0053] Where f(x,y) is the input object information, * represents convolution, g(x,y) is the inclusion system imaging, h(x,y) is the point spread function of the sparse aperture optical system, and n(x,y) is the noise in the imaging process. In Fourier transform space, the above formula is expressed as

[0054] G(u,v)=F(u,v)H(u,v)+N(u,v) (2)

[0055] Where H(u,v) is the Fourier transform of h(x,y), which is the optical transfer function. The optical transfer function is usually a complex number and can be decomposed into two parts: amplitude and phase. The amplitude part is called the modulation transfer function (MTF) and the phase part is called the phase transfer function (PTF). Their relationship is shown in the following formula.

[0056] H(u,v)=MTF(u,v)exp[jPTF(u,v)] (3)

[0057] where j is the imaginary unit.

[0058] Since the effective light transmission area of ​​the sparse aperture system is smaller than that of the system with the same effective aperture, the imaging quality is reduced and the image is blurred. The Wiener filtering method is usually used to improve the imaging clarity. The Wiener filtering is expressed as

[0059]

[0060] Among them, H * (u,v) is the conjugate function of H(u,v), That is the restored image. For the sparse aperture system that has been processed, the optical transfer function of its ideal working state can be obtained, and the imaging quality can be improved by Wiener filtering. However, the processing equipment process and the working process may cause the sparse aperture system components to tilt, displace, and deform, and the optical transfer function will change, and the Wiener filter imaging restoration effect will deteriorate. Therefore, in order to solve the problem of difficulty in image quality restoration caused by errors in sparse aperture optical system components, the focus is on obtaining the changed optical transfer function.

[0061] Sparse aperture systems usually use total reflection or catadioptric optical components, and have a wide operating band. Formulas (1)-(2) are applicable to imaging at each single wavelength, and are independent of each other at each wavelength. For ease of explanation, the present invention only introduces the invention content for a single wavelength. In addition, when noise is not considered, it can be obtained from Formulas (2) and (3):

[0062] |G(u,v)|=|F(u,v)|MTF(u,v) (5)

[0063] angle[G(u,v)]=angle[F(u,v)]+PTF(u,v) (6)

[0064] To this end, the present invention establishes two convolutional neural networks, one for the amplitude part, to establish the corresponding relationship between the system imaging amplitude and the modulation transfer function, and the other for the phase part, to establish the corresponding relationship between the system imaging phase and the phase transfer function, thereby obtaining the mapping relationship between the system imaging and the optical transfer function. When restoring the image, the Fourier transform of the system imaging is input into the trained convolutional neural network to obtain the optical transfer function, and then the Wiener filter imaging restoration is performed.

[0065] The present invention proposes a sparse aperture system imaging restoration method, comprising the following steps:

[0066] (1) Establish a database of sparse aperture system imaging and corresponding optical transfer functions to prepare data for convolutional network training and learning. Use the optical design software ZEMAX to establish a sparse aperture system simulation system. The optical surfaces of the system mainly have conditions such as tilt, displacement, and curvature radius change, which cause changes in the optical transfer function. ZEMAX software has the function of outputting the point spread function data of the simulated optical system. To this end, the software is used to simulate various tilt, displacement, and curvature radius change conditions of the optical surface, and the point spread function under each condition is obtained through the software, and the modulation transfer function and phase transfer function are further calculated.

[0067] The process of this step is as follows Figure 1 As shown, specifically including:

[0068] Step 1: Simulate the sparse aperture optical system. According to the component parameters of the sparse aperture optical system, mainly the radius of the optical surface, the spacing, and the medium refractive index, a simulation system is established in the ZEMAX software.

[0069] Step 2, set the error range of optical surface parameters. Usually, the tilt, displacement, and curvature radius of the optical surface change very small. The tilt will rotate around the x, y, and z axes passing through the vertex of the optical surface. The rotation angle range is [-0.01°, 0.01°], and the values ​​are taken at equal intervals of 0.005° as the step size, with a total of 5 values, and a total of 125 values ​​for the three axes. The displacement range along the x, y, and z directions is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ as the step size, λ is the wavelength, with a total of 11 values, and a total of 1331 values ​​for the three axes. The curvature radius change range is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ as the step size, λ is the wavelength, with a total of 11 values, so an optical surface has approximately 1830125 errors. For a system with Golay3 and three sub-mirrors, there may be 6.1×10 18 Kind of error.

[0070] Step 3, simulate and obtain the sparse aperture system imaging and the corresponding optical transfer function. Using the extended programming method of ZEMAX software, simulate various optical surface errors within the error range of step 2, and output the corresponding modulation transfer function and phase transfer function. For the selected target, obtain the corresponding sparse aperture system imaging under various error conditions. Thus, the corresponding relationship between the sparse aperture system imaging and the modulation transfer function and phase transfer function is established.

[0071] (2) Constructing a deep neural network mainly involves determining the network structure, activation function, and loss function. Two deep convolutional neural networks are constructed. One is called the amplitude deep neural network, which establishes the corresponding relationship between the amplitude of the system imaging Fourier transform and the modulation transfer function. The other is called the phase deep neural network, which establishes the corresponding relationship between the phase of the system imaging and the phase transfer function.

[0072] The pixel values ​​of the input sparse aperture image are normalized to a number between 0 and 1, and then Fourier transform is performed to obtain its amplitude as the input of the amplitude deep neural network. The phase angle is obtained as the input of the phase deep neural network. The following mainly describes the network structure for the amplitude deep neural network, such as Figure 2 As shown, the phase deep neural network is similar.

[0073] The amplitude deep neural network includes 5 convolutional layers, 1 nonlinear regression layer, and finally outputs the modulation transfer function.

[0074] In the first convolution layer, three different scales of convolution kernels are used to convolve the input amplitude data matrix to extract the features of the input matrix. Each scale uses 20 convolution surfaces, each with a bias. The feature extraction obtains 20 matrices, each of which is a group of 5 matrices. The maximum value of the corresponding element is used as the output, and 4 matrices are obtained. The process is expressed as

[0075]

[0076] Where W is the convolution kernel, I is the input amplitude data matrix, and b is the bias. i is the scale number. When i=0, 1, 2, the convolution kernel size is 3×3, 5×5, and 7×7 respectively. k∈[0,4], each group of 5 matrices takes the maximum value of the corresponding element as the output, and the MAX function means taking the maximum value of the corresponding element. We get 4 M×N matrices on each of the 3 scales.

[0077] In the second convolution layer, for each scale, four 7×7 convolution kernels are used to convolve the matrix of the first layer. Each convolution uses a bias to further extract features. The activation function uses the ReLU function. The average value of the four matrices is taken as the output, and three M×N matrix groups are obtained. The process is expressed as

[0078]

[0079] In the third convolution layer, three 5×5 convolution kernels are used to convolve the matrices of the second layer. Each convolution uses a bias, uses the ReLU function as the activation function, and averages the three matrices. The output is a matrix of size M×N. The process is expressed as

[0080]

[0081] In the 4th and 5th convolution layers, 3×3 convolution kernels are used to convolve the results of the previous layer. Each convolution uses a bias, and all use the ReLU function as the activation function and perform normalization to speed up network training. The process is expressed as

[0082] P k(u,v)=normal{Relu[W k *P k-1 (u,v)+b k ]}, where k = 4, 5 (10) where the normal function represents the normalization process.

[0083] The sixth layer is a nonlinear regression layer, which uses a 3×3 convolution kernel to convolve the results of the previous layer, and then uses an activation function to process the convolution results so that the output value is between 0 and 1. The process is expressed as

[0084] P6(u,v)=min{max(W 6 *P5(u,v)+b 6 ,0),1} (11)

[0085] The max() function is used to find the maximum value of two values, and the min() function is used to find the minimum value of two values. The output is the atmospheric modulation transfer function obtained.

[0086] For the phase deep neural network, the activation function of the 6th layer is adopted as formula (12), where t is the input value, and the phase transfer function is obtained Its range is (-π, π]. According to formula (13), the optical transfer function is obtained

[0087]

[0088]

[0089] The loss function of the network system adopts the root mean square value of the difference between the ideal transfer function and the transfer function of the network output under each error state, where the loss functions of the amplitude deep neural network and the phase deep neural network are shown in the following formula.

[0090]

[0091]

[0092] (3) Use the training set to train the convolutional neural network. For the training set data, set the initial value, learning rate, and formulate a learning rate change strategy, and input the target image into the neural network to carry out network training.

[0093] (4) Imaging restoration of sparse aperture systems based on optical transfer functions. Figure 3As shown, the pixel values ​​of the image obtained by imaging the sparse aperture system are normalized to numbers between 0 and 1. After the image is Fourier transformed, its modulus and phase angle are taken, and after normalization, they are input into the corresponding neural network respectively, and their respective transfer functions are calculated and merged into the optical transfer function. After the image obtained by imaging the sparse aperture system is Fourier transformed, the optical transfer function is used to perform image restoration processing according to formula (3), and the result is inverse Fourier transformed, that is, the imaging result is restored.

[0094] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0095] Embodiment 1

[0096] like Figure 4 The figure shows a Golay3 sparse aperture optical system, which consists of a primary mirror and a secondary mirror. The primary mirror is replaced by three sub-mirrors. When the parameters of each sub-mirror are error-free, when the system observes Figure 5 When the object plane information is shown, the image is obtained as Figure 6 As shown. It can be seen that the image is blurred and the color is dim. This is because the actual aperture area is smaller than the full aperture system and the light flux is insufficient. At this time, the modulation transfer function and phase transfer function of the system are obtained as follows Figure 7 , 8 As shown, Figure 7 Displayed in false color, the phase angle range is (-π, π], for this Figure 8 The phase values ​​are shown after normalization to [0,1].

[0097] Embodiment 2

[0098] To illustrate the effect of this example, Fig. 9 The resolution board shown is used as the object plane scene. When the system sub-mirror 1 rotates 0.005° around the x-axis, the modulation transfer function MTF and phase transfer function PTF obtained by system simulation are as follows Fig.10 , 11 As shown in Figure 2, the simulation results are as follows: Fig.12 As shown, compared with the error-free case, the image is very blurred and the resolution is very low. When the sub-mirror 2 rotates 0.005° around the x-axis, the modulation transfer function MTF and phase transfer function PTF obtained by system simulation are as follows Fig.13 , 14 As shown in Figure 2, the simulation results are as follows: Fig.15 As shown, it can be seen that although the same sub-mirror is tilted at the same angle, the MTF and PTF data obtained twice are different, and the imaging results are also different.

[0099] When the sub-mirror 1 is displaced by 0.005 mm along the y-axis, the modulation transfer function MTF and phase transfer function PTF obtained by system simulation are as follows: Fig.16 , 17As shown in Figure 2, the simulation results are as follows: Fig.18 When the sub-mirror 2 is displaced by 0.005 mm along the y-axis, the modulation transfer function MTF and phase transfer function PTF obtained by simulation are as follows: Fig.19 , 20 As shown in Figure 2, the simulation results are as follows: Fig.21 As shown in the figure, it can be seen that although the sub-mirror is displaced the same distance along the y-axis, the MTF and PTF data obtained twice are different, and the imaging results are also different.

[0100] This example shows that different sub-mirror errors produce different modulation transfer function MTF and phase transfer function PTF, and the imaging results are all different. Therefore, there is a mapping relationship between sub-mirror error parameters, imaging results, modulation transfer function MTF, and phase transfer function PTF.

[0101] Embodiment 3

[0102] use Figure 5 For the object scene, when the system sub-mirror 1 rotates 0.005° around a certain axis, the image obtained by the system is as follows Fig. 22 As shown, Figure 6 More and more blurred. Figure 7 and Figure 8 The optical transfer function is used to restore the image. The result is as follows Fig.23 As shown in Figure 1, it can be seen that the restoration effect is not ideal. The modulation transfer function MTF and phase transfer function PTF estimated by deep convolutional neural network are shown in Figure 1. Fig.24 , 25 As shown, the image is restored and the result is as follows Fig.26 As shown, it can be seen that the recovery effect is significantly improved.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A sparse aperture system imaging restoration method, comprising the following steps: Step 1: Establish a database of sparse aperture system imaging and corresponding optical transfer functions; Step 2: Build a deep neural network, including determining the network structure, activation function, and loss function; Step 3: Use the training set to train the convolutional neural network; Step 4: Realize sparse aperture imaging restoration based on optical transfer function; In the step 1, the optical design software ZEMAX is used to establish a sparse aperture system simulation system, through which various tilt, displacement, and curvature radius change conditions of the optical surface are simulated, and the point spread function under each condition is obtained by the software, and the modulation transfer function and the phase transfer function are calculated; The step 1 comprises: Step 1-1: Simulate the sparse aperture optical system. According to the component parameters of the sparse aperture optical system, establish a simulation system in ZEMAX software; Step 1-2: Set the error range of optical surface parameters, rotate around the x, y, and z axes passing through the vertex of the optical surface, the rotation angle range is [-0.01°, 0.01°], and the values ​​are taken at equal intervals of 0.005°, with a total of 5 values, and a total of 125 values ​​for the three axes. The displacement range along the x, y, and z directions is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ, λ is the wavelength, and a total of 11 values, and a total of 1331 values ​​for the three axes. The curvature radius change range is [-λ, λ], and the values ​​are taken at equal intervals of 0.2λ, λ is the wavelength, and a total of 11 values; Step 1-3: Using the extended programming method of ZEMAX software, various optical surface errors are simulated within the error range of step 2, and the corresponding modulation transfer function and phase transfer function are output. For the selected target, the corresponding sparse aperture system imaging under various error conditions is obtained, thereby establishing the corresponding relationship between the sparse aperture system imaging and the modulation transfer function and phase transfer function; The step 2 comprises: normalizing the pixel value of the image formed by the input sparse aperture system to a number between 0 and 1, calculating the modulus of its Fourier transform to obtain its amplitude as the input of the amplitude deep neural network; calculating its phase angle as the input of the phase deep neural network; The step 3 includes: for the training set data, setting the initial value, the learning rate, and formulating a learning rate change strategy, inputting the target image into the neural network to carry out network training; The step 4 comprises: normalizing the pixel values ​​of the image obtained by imaging the sparse aperture system to a number between 0 and 1, performing Fourier transform on the image, taking its modulus and phase angle, and inputting them into corresponding neural networks after normalization, calculating their respective transfer functions, and merging them into an optical transfer function; performing Fourier transform on the image obtained by imaging the sparse aperture system, using the optical transfer function to perform image restoration processing, and performing inverse Fourier transform on the result to obtain an imaging restoration result.

Images