A method for restoring a turbulence-degraded image based on complex amplitude detection
By reconstructing wavefront complex amplitude and Fresnel diffraction imaging models through an end-to-end neural network and combining them with a multi-scale deconvolution network, the problems of high cost of hardware correctors and difficulty in obtaining labeled data are solved, achieving low-cost and high-precision restoration of turbulent degradation images, which is suitable for astronomical observation and long-distance imaging.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF OPTICS & ELECTRONICS CHINESE ACAD OF SCI
- Filing Date
- 2026-05-29
- Publication Date
- 2026-06-26
Smart Images
Figure CN122289083A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computational optical imaging technology, specifically relating to a method for restoring turbulent degradation images based on complex amplitude detection. Background Technology
[0002] In fields such as astronomical observation, long-distance imaging, and space target monitoring, atmospheric turbulence can cause random spatiotemporal fluctuations in the air refractive index, which in turn causes distortions in the phase and amplitude of the beam wavefront. Ultimately, this leads to degradation phenomena such as blurring, jitter, and geometric distortion in the target images captured by the imaging system, severely affecting the accuracy of subsequent image analysis and target recognition.
[0003] Currently, the mainstream technology for suppressing the effects of atmospheric turbulence is hardware adaptive optics. Its core is to detect wavefront distortion in real time using a wavefront sensor, and then use a controller to drive correction units such as deformable mirrors to perform wavefront compensation, thereby improving image quality. However, this technology has the following inherent drawbacks: First, the system architecture is complex and the hardware cost is high, making it difficult to widely apply; second, the physical travel of the corrector is limited, resulting in insufficient correction capability in strong turbulence and large aberration scenarios; third, closed-loop correction has inherent time delays, making it difficult to adapt to high-speed, dynamically changing turbulent environments; and fourth, even after hardware correction, the acquired image still requires post-processing to achieve ideal quality.
[0004] To overcome the aforementioned problems, computational optics imaging technology has received widespread attention in recent years. Among them, computational adaptive optics without wavefront correction has become a research hotspot due to its advantages such as low cost, no correction travel limit, and no time delay. Existing methods mostly adopt the approach of combining wavefront sensing and deconvolution, and iteratively infer the phase between the target object and the wavefront by alternately minimizing the wavefront. However, these methods still have significant shortcomings: on the one hand, most methods only focus on wavefront phase estimation and ignore wavefront amplitude information, resulting in insufficient integrity of wavefront detection; on the other hand, traditional iterative algorithms have high computational complexity and are prone to amplifying imaging noise, affecting the reconstruction accuracy.
[0005] In recent years, deep learning technology has made significant progress in wavefront reconstruction and image restoration. However, most existing deep learning methods rely on large amounts of paired labeled data for training, such as Hartmann image-wavefront phase sample pairs and sharp target image-turbulent degradation image sample pairs. In actual atmospheric turbulence observation scenarios, it is difficult to obtain such high-precision real-world labeled data, especially to directly obtain accurate ground truth wavefront phase values and ideal sharp target images.
[0006] In summary, how to achieve efficient and high-precision restoration of turbulent degradation images without relying on hardware correctors or requiring comprehensive and accurate labeled data has become a pressing technical challenge in this field. Summary of the Invention
[0007] To address the aforementioned technical problems, this invention provides a method for restoring turbulent degradation images based on complex amplitude detection. This method takes synchronously aligned Hartmann images and target degradation images as inputs, constructs an end-to-end neural network architecture based on physical constraints, and achieves accurate inference from Hartmann images to the point spread function of the imaging system by reconstructing wavefront complex amplitudes. Finally, it realizes high-quality reconstruction of turbulent degradation images in a multi-scale deconvolution network.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] A method for restoring turbulence degradation images based on complex amplitude detection includes:
[0010] Step 1: Input the Hartmann image of the point target into the wavefront reconstruction network. The wavefront reconstruction network adopts an encoder-decoder structure and outputs wavefront complex amplitude information that simultaneously contains amplitude distribution and phase distribution.
[0011] Step 2: Input the wavefront complex amplitude information into the Fresnel diffraction imaging model, solve for the initial imaging point spread function, input the initial imaging point spread function into a lightweight convolutional neural network for fine correction, and output the estimated imaging point spread function.
[0012] Step 3: Input the estimated imaging point spread function and the turbulence degradation image into a multi-scale deconvolution network. The multi-scale deconvolution network is based on the UNet architecture. A Wiener filter module is embedded in each skip connection branch between the encoder and the decoder. A multi-scale point spread function is generated based on the estimated imaging point spread function and sent to the Wiener filter module of the corresponding level. After the decoder fuses the multi-scale features, a clear restored image is output.
[0013] Furthermore, in step 1, the encoder of the wavefront reconstruction network has six levels, each containing two layers of 3×3 convolutions for feature extraction, a linear rectified activation function for nonlinear mapping, and max pooling for double downsampling; the decoder also has six levels, each using two layers of 3×3 convolutions and a linear rectified activation function, upsampling through transposed convolutions, and fusion of shallow details from the encoder and deep features from the decoder through skip connections.
[0014] Furthermore, in step 1, the training process of the wavefront reconstruction network uses the reference wavefront phase as a constraint to construct a first loss function based on mean square error. The first loss function is defined as a measure of the difference between the reference wavefront phase and the reconstructed wavefront phase. The network parameters are iteratively optimized through the backpropagation algorithm, so that the wavefront reconstruction network learns the nonlinear mapping relationship from the point target Hartman image to the wavefront phase.
[0015] Furthermore, in step 2, the lightweight convolutional neural network adopts a one-level encoder and one-level decoder structure, and the network structure of each level of the one-level encoder and one-level decoder is consistent with the structure of the wavefront reconstruction network.
[0016] Furthermore, in step 2, during the training phase of the lightweight convolutional neural network, a second loss function is constructed using the real point target degradation image as the ground truth. The second loss function is the mean square error between the real point target degradation image and the estimated imaging point diffusion function.
[0017] Furthermore, joint backpropagation optimization is performed on the wavefront reconstruction network and the lightweight convolutional neural network, and the loss weight of the first loss function is lower than the loss weight of the second loss function.
[0018] Furthermore, in step 3, the multi-scale deconvolutional network is configured with a five-level encoder and a five-level decoder. The encoder uses average pooling to perform downsampling, and a Wiener filter module is embedded in each skip connection branch between the encoder and the decoder. Based on the estimated imaging point spread function, a multi-scale point spread function matching the feature map of each layer of the network is generated by progressively averaging downsampling, and then fed into the Wiener filter module of the corresponding layer to construct a multi-scale feature deconvolution unit under physical prior constraints.
[0019] Furthermore, the forward inference process of the multi-scale deconvolutional network is as follows: First, the encoder extracts multi-scale deep features of the turbulent degradation image step by step to suppress noise interference in the degradation image; then, in the skip connection branch, relying on the Wiener filtering module at each scale and combined with the prior point spread function information of the corresponding level, the initial restoration of the degradation image is completed; finally, the decoder fuses the multi-scale features and completes image reconstruction, eliminating the blur and distortion caused by atmospheric turbulence, and outputting a clear restored image.
[0020] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for restoring turbulent degradation images based on complex amplitude detection.
[0021] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for restoring turbulent degradation images based on complex amplitude detection.
[0022] The beneficial effects of this invention are as follows:
[0023] Low hardware cost and significantly reduced system complexity: This invention constructs a computational optical imaging system that eliminates the hardware correction unit, requiring only the wavefront sensor and the imaging sensor to work together. It eliminates the expensive deformable mirror and its control system in traditional adaptive optics technology, greatly reducing system cost and complexity. At the same time, it breaks through the limitation of physical correction stroke and is suitable for turbulent scenarios of different intensities.
[0024] High wavefront detection integrity and improved restoration accuracy: This invention achieves complex amplitude reconstruction for the first time in a wavefront-free correction system, simultaneously restoring both the phase and amplitude information of the wavefront, overcoming the shortcomings of traditional methods that only focus on phase estimation. Based on the reconstructed complex amplitude data, combined with the Fresnel diffraction physical model, the point spread function of the imaging system can be accurately derived, laying the foundation for high-precision image restoration.
[0025] End-to-end training reduces reliance on real labeled data: This invention designs an end-to-end neural network architecture based on physical constraints. Through physical model constraints, only the paired data of the point target Hartmann image and the corresponding degraded image are needed to achieve high-precision reconstruction of wavefront complex amplitude and high-quality reconstruction of the target. This reduces the need for some labeled data and effectively solves the problem of difficulty in obtaining real turbulence phase data and clear target data.
[0026] Highly adaptable and with broad application prospects: This invention is applicable to extreme scenarios such as strong turbulence and large aberrations, and can achieve low-cost, high-efficiency high-resolution image acquisition in fields such as astronomical observation, space target monitoring, and long-distance imaging. Attached Figure Description
[0027] Figure 1 This is a schematic diagram of the optical system required for implementing the turbulence degradation image restoration method based on complex amplitude detection according to the present invention.
[0028] Figure 2 This is a network schematic diagram of a turbulence degradation image restoration method based on complex amplitude detection according to the present invention.
[0029] Figure 3 This invention demonstrates the image restoration effect of point targets degraded under different turbulence intensities. Detailed Implementation
[0030] The invention will now be further described with reference to the accompanying drawings.
[0031] This invention provides a method for restoring turbulent degradation images based on complex amplitude detection, aiming to address the technical challenges of high cost, limited correction range, and time delay inherent in traditional hardware adaptive optics techniques. This invention constructs a computational optics imaging system that eliminates the hardware correction unit. It relies on a wavefront sensor and an imaging sensor to simultaneously acquire wavefront data and target degradation images. A computational processing unit reconstructs the wavefront complex amplitude and corrects aberrations. Based on this, a physically constrained end-to-end neural network architecture is designed. By reconstructing the wavefront complex amplitude, it achieves accurate mapping and inference from the Hartmann image to the system point spread function. Finally, a multi-scale deconvolutional network is combined to complete high-quality restoration of the turbulent degradation image.
[0032] like Figure 1 As shown, the computational optics imaging system of this invention includes a wavefront sensor, an imaging system, and a computational processing unit. The wavefront sensor and the imaging sensor acquire data using a synchronous triggering mechanism, possessing delay-free wavefront sensing and aberration correction characteristics. The wavefront sensor is used to acquire Hartmann images, and the imaging sensor of the imaging system is used to acquire degraded images of the target affected by turbulence. The two data streams must have spatiotemporal consistency to provide aligned input for subsequent complex amplitude reconstruction and image restoration.
[0033] The experimental platform includes an imaging light source, a Hartmann sensor, a reflector, a lens, a beam splitter, a photoelectric detection system, and a computational processing module. A visible light laser point source simulates a target. After being modulated by simulated turbulence of varying intensities, the beam carrying distortion information is split into two paths by an optical beam splitter. One path is fed into the Hartmann wavefront sensor to detect the wavefront slope information, while the other path enters the imaging system to acquire a turbulently degraded image of the target. The acquired wavefront signal and the degraded image are input into the computational processing module, where an end-to-end restoration algorithm is used to reconstruct the wavefront complex amplitude, estimate the point spread function of the imaging system, and reconstruct the target image.
[0034] For the adaptive optics system without a wavefront correction unit of this invention, the wavefront sensor and the imaging system synchronously acquire light field information, jointly estimate the turbulent wavefront and the imaging target, and calculate the complex amplitude data of the wavefront distortion and the point spread function (PSF) corresponding to the imaging system. Then, by using the method of deconvolution and deep learning fusion, the blurred image acquired by the camera affected by the wavefront distortion is sharpened and restored.
[0035] In the process of target image degradation caused by atmospheric turbulence, let the spatial coordinates of the imaging plane be... At this location, the ideal image of the target is The point spread function of the optical system is The noise introduced by the signal detection environment and camera is Therefore, the far-field image is degraded due to turbulence. It can be modeled as a convolutional model:
[0036] ,
[0037] For imaging distant targets, the point spread function satisfies spatial translation invariance, and Wiener filtering can be used to achieve fast deconvolution, restoring the image as follows. :
[0038] ,
[0039] in, This represents the Fourier transform operator from the time domain to the frequency domain. This corresponds to the inverse Fourier transform; Represents the complex number conjugate operation. It represents the Hadamardi (or Hadama) stack. The regularization parameter is adjusted by... The value of can strike a balance between noise suppression and image detail preservation.
[0040] Therefore, the key to achieving clear image restoration lies in obtaining an accurate point spread function. This can be achieved by analyzing noisy Hartman images obtained through wavefront probing. Inversion is performed to extract complex amplitude information, which is then used to reconstruct the wavefront amplitude (intensity distribution). With phase distribution ,Right now:
[0041] ,
[0042] Then, using the Fresnel diffraction integral, the system point spread function is calculated:
[0043] ,
[0044] In the formula, Let the pupil plane coordinates be the coordinates. Represents the Fresnel diffraction operator with a propagation distance of d. It represents the imaginary unit.
[0045] This invention characterizes atmospheric turbulence as an equivalent complex amplitude perturbation of the pupil surface and models the imaging system as a forward convolutional degradation model, providing physical constraints for deep learning networks by introducing the aforementioned prior physical knowledge. Figure 2 As shown, this invention proposes a method for restoring turbulent degradation images based on complex amplitude detection. This method is implemented based on an end-to-end deep neural network and includes three steps: wavefront complex amplitude reconstruction, imaging point spread function estimation, and turbulent degradation image restoration. The specific steps are as follows:
[0046] Step 1: Reconstruct the wavefront complex amplitude based on the UNet network.
[0047] The Hartmann image of the point target is input into a wavefront reconstruction network (UNet), which employs an encoder-decoder structure. The encoder consists of six levels, each containing two 3×3 convolutional layers for feature extraction, a ReLU activation function for non-linear mapping, and max pooling for 2x downsampling, progressively mining multi-scale features from the image. The decoder also consists of six levels, each using two 3×3 convolutional layers and a ReLU activation function. Transposed convolutions are used for upsampling to restore the feature map size, and skip connections are used to fuse shallow details from the encoder with deep features from the decoder. The final network output includes both amplitude distribution and waveform. With phase distribution Wavefront complex amplitude information; during network training, the first loss function is constructed using the reference wavefront phase as the ground truth. In the formula, Let be the mean square error function. The reference wavefront phase is obtained by using the direct slope method. The reconstructed wavefront phase is output by the UNet network. The network parameters are iteratively optimized using the backpropagation algorithm, enabling the network to learn the nonlinear mapping relationship from the noisy Hartman image to the wavefront phase. While the reference wavefront phase differs from the true wavefront, it effectively constrains the network training process, stabilizes the network convergence direction, and provides a reasonable complex wavefront amplitude input for the subsequent step 2.
[0048] It is worth noting that the point target Hartmann image described in this invention refers to a Hartmann image acquired by a wavefront sensor after the light emitted from a target (such as a natural star, a distant point source, or an artificial beacon) in the imaging field of view has been disturbed by atmospheric turbulence. A point target is used because the wavefront distortion of a point source can directly reflect the complex amplitude disturbance caused by turbulence. The point spread function of the imaging system can be inverted from a single frame Hartmann image without prior knowledge of the target's structural information. For extended targets (such as satellites and aircraft), their Hartmann images contain superimposed information about the target's own structure, making them unsuitable for independent estimation of the point spread function. Therefore, during system deployment or data acquisition, this invention requires ensuring the presence of a known or identifiable point source in the field of view to obtain the corresponding point target Hartmann image.
[0049] Step 2: Achieve accurate estimation of the point spread function through a physical imaging model and an optimized network.
[0050] The wavefront complex amplitude output in step 1 Input the Fresnel diffraction imaging model, according to the formula The initial imaging PSF is obtained by solving the equation. To suppress the systematic bias and approximation error introduced by the physical imaging model itself, a lightweight convolutional neural network (CNN) is introduced to further refine the initial PSF. This CNN adopts a 1-level encoder and 1-level decoder structure, and the network structure and parameter settings of each level are consistent with the UNet in step 1, resulting in a more accurate estimated PSF output.
[0051] During the training phase, a second loss function is constructed using the degraded point target image as the ground truth. In the formula, A degraded image of a real point target. The estimated imaging PSF is obtained by inputting the reconstructed wavefront complex amplitude into the imaging model and optimizing it with a CNN. The wavefront reconstruction network and the optimized CNN network are jointly optimized by backpropagation. The information of the real degraded image is used to constrain the wavefront reconstruction process, thereby improving the matching accuracy between the PSF estimate and the actual imaging degradation process.
[0052] Since the core objective of this method is to accurately estimate the PSF, the loss weight of L1 is set to be significantly lower than that of L2. The network parameters in steps 1 and 2 are updated synchronously to jointly complete the end-to-end accurate modeling from the wavefront sensing end to the far-field imaging end.
[0053] Step 3: Restore the turbulent degradation image based on a multi-scale deconvolution network.
[0054] The estimated PSF obtained in step 2 is input together with the turbulence degradation image into a multi-scale deconvolutional network (MWDN). This network is based on the UNet architecture, with a 5-level encoder and a 5-level decoder. The encoder uses average pooling for downsampling. The remaining network layers, kernel size, activation functions, and hyperparameter configurations are consistent with the UNet proposed in step 1. The core design of the MWDN network lies in embedding a Wiener filter module in each skip connection branch between the encoder and decoder. Based on the standard-scale PSF estimated in step 2, a multi-scale PSF matching the feature maps of each network level is generated through progressively averaging downsampling. These multi-scale PSFs are then fed into the corresponding Wiener filter modules, thus constructing multi-scale feature deconvolution units under physical prior constraints.
[0055] During the forward inference process, the encoder first extracts multi-scale deep features of the turbulent degradation image level by level to suppress noise interference in the degradation image. Then, in the skip connection branch, relying on Wiener filtering modules at each scale and combining the prior PSF information of the corresponding level, the degradation image is initially restored. Finally, the decoder fuses the multi-scale features and completes image reconstruction, gradually eliminating the blurring and distortion caused by atmospheric turbulence, and finally outputting a clear restored image. This multi-scale deconvolution architecture can simultaneously adapt to the degradation characteristics of turbulence of different intensities, effectively suppressing amplified noise while preserving the target detail features, and achieving end-to-end turbulent degradation image restoration.
[0056] To verify the effectiveness of this method, point target reconstruction experiments were conducted on simulation data under different turbulence intensities (telescope aperture set to 1.8m). The experimental results are as follows: Figure 3 As shown, the horizontal axis represents the atmospheric coherence length r0 (in cm), and the vertical axis represents the full width at half maximum (FWHM, in pixels) of the restored spot. The results show that under turbulence intensities ranging from 3 cm to 8 cm, the FWHM of the restored spot using this method remains stable at approximately 4.56 pixels, with relatively small overall fluctuations, achieving effective wavefront aberration correction. Compared to the diffraction-limited spot (FWHM = 2.65 pixels), the restoration result achieved is approximately 1.7 times the diffraction-limited imaging effect.
[0057] In summary, this invention provides a method for restoring turbulent degraded images based on complex amplitude detection. By simplifying the hardware architecture, integrating physical models and deep learning, and constructing an end-to-end optimization framework, it effectively solves the image degradation problem caused by atmospheric turbulence, and provides an efficient and reliable technical solution for high-resolution imaging in adaptive optics systems.
[0058] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for restoring turbulent degradation images based on complex amplitude detection.
[0059] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for restoring turbulent degradation images based on complex amplitude detection.
[0060] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for restoring turbulent degradation images based on complex amplitude detection, characterized in that, include: Step 1: Input the Hartmann image of the point target into the wavefront reconstruction network. The wavefront reconstruction network adopts an encoder-decoder structure and outputs wavefront complex amplitude information that simultaneously contains amplitude distribution and phase distribution. Step 2: Input the wavefront complex amplitude information into the Fresnel diffraction imaging model, solve for the initial imaging point spread function, input the initial imaging point spread function into a lightweight convolutional neural network for fine correction, and output the estimated imaging point spread function. Step 3: Input the estimated imaging point spread function and the turbulence degradation image into a multi-scale deconvolution network. The multi-scale deconvolution network is based on the UNet architecture. A Wiener filter module is embedded in each skip connection branch between the encoder and the decoder. A multi-scale point spread function is generated based on the estimated imaging point spread function and sent to the Wiener filter module of the corresponding level. After the decoder fuses the multi-scale features, a clear restored image is output.
2. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 1, characterized in that, In step 1, the encoder of the wavefront reconstruction network has six levels. Each level contains two layers of 3×3 convolutions for feature extraction, a linear rectified activation function for nonlinear mapping, and max pooling for downsampling. The decoder also has six levels. Each level uses two layers of 3×3 convolutions and a linear rectified activation function. Upsampling is achieved through transposed convolutions, and skip connections are used to fuse shallow details from the encoder with deep features from the decoder.
3. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 1, characterized in that, In step 1, the training process of the wavefront reconstruction network uses the reference wavefront phase as a constraint to construct a first loss function based on mean square error. The first loss function is defined as a measure of the difference between the reference wavefront phase and the reconstructed wavefront phase. The network parameters are iteratively optimized through the backpropagation algorithm, so that the wavefront reconstruction network learns the nonlinear mapping relationship from the point target Hartman image to the wavefront phase.
4. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 1, characterized in that, In step 2, the lightweight convolutional neural network adopts a one-level encoder and one-level decoder structure, and the network structure of each level of the one-level encoder and one-level decoder is consistent with the structure of the wavefront reconstruction network.
5. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 3, characterized in that, In step 2, during the training phase of the lightweight convolutional neural network, a second loss function is constructed using the real point target degraded image as the ground truth. The second loss function is the mean square error between the real point target degraded image and the estimated imaging point spread function.
6. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 5, characterized in that, Joint backpropagation optimization is performed on the wavefront reconstruction network and the lightweight convolutional neural network, and the loss weight of the first loss function is lower than the loss weight of the second loss function.
7. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 1, characterized in that, In step 3, the multi-scale deconvolutional network is configured with a five-level encoder and a five-level decoder. The encoder uses average pooling to perform downsampling. A Wiener filter module is embedded in each skip connection branch between the encoder and the decoder. Based on the estimated imaging point spread function, a multi-scale point spread function matching the feature map of each layer of the network is generated by progressively averaging downsampling. These functions are then fed into the Wiener filter module of the corresponding layer to construct a multi-scale feature deconvolution unit under physical prior constraints.
8. The method for restoring turbulent degradation images based on complex amplitude detection according to claim 7, characterized in that, The forward inference process of the multi-scale deconvolutional network is as follows: First, the encoder extracts multi-scale deep features of the turbulent degradation image step by step to suppress noise interference in the degradation image; then, in the skip connection branch, the Wiener filter module at each scale and the prior point spread function information of the corresponding level are used to complete the preliminary restoration of the degradation image; finally, the decoder fuses the multi-scale features and completes the image reconstruction, eliminating the blur and distortion caused by atmospheric turbulence, and outputting a clear restored image.
9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the turbulence degradation image restoration method based on complex amplitude detection as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the turbulence degradation image restoration method based on complex amplitude detection as described in any one of claims 1-8.