Image reconstruction method and system for ground-based solar telescope under weak vision comfort

Abstract

The application provides a weak vision ground-based solar telescope image reconstruction method and system, and belongs to the technical field of space remote sensing detection. The method does not need to perform a recursive process to calculate the image phase like the image spot masking method, so it will not accumulate noise errors, and the reconstructed image results will not appear false structure. According to the non-rigid aligned short exposure solar image, the sub-block processing is performed, and through the improved lucky frame selection method, a part of the images with serious geometric structure error are excluded, and the sub-block images with more stable structure and more high-frequency information are selected. An initial phase iteration value can be solved according to the lucky sub-block image, and then the optimization method is used to start iteration from the initial phase value, and after the iteration number is set, the accurate phase information is finally calculated. Thus, the actual system instantaneous transfer function psf of each sub-block can be restored, and the solar image with better quality can be reconstructed.

Description

Technical Field

[0001] This invention belongs to the field of space remote sensing technology, specifically relating to a method, reconstruction system, electronic equipment, readable storage medium, and computer program product for reconstructing images from a ground-based solar telescope under low visibility conditions. Background Technology

[0002] Seeing refers to the sharpness of an image displayed by a telescope. It depends on the degree of atmospheric turbulence. The twinkling of celestial bodies visible to the naked eye is generally considered to be caused by turbulence in the upper atmosphere. Poor telescope sharpness is often caused by turbulence in the lower atmosphere. Turbulence in different layers of the atmosphere creates unstable regions of varying densities, preventing light from passing through smoothly and maintaining a constant intensity.

[0003] Atmospheric turbulence has always been a major factor limiting the resolution of imaging systems when ground-based solar telescopes conduct target observations. Fluctuations in the atmospheric refractive index caused by turbulence result in wavefront fluctuations in the incident light from the target, leading to blurring, severe distortion, random displacement, and fragmentation in the solar short-exposure blob images acquired by the telescope. Reconstructing high-resolution images from solar short-exposure blob images is a crucial task for ground-based solar telescopes. Under conditions of intense atmospheric turbulence, the atmospheric seeing parameter r0 can drop below 6 cm, making high-resolution reconstruction of target images impossible with existing algorithms. The large amount of solar short-exposure blob image data observed under weak seeing conditions cannot be reconstructed satisfactorily, which is unreasonable for ground-based solar telescopes. Currently, there are three main existing technologies for image reconstruction from ground-based solar telescopes:

[0004] Technique 1: Utilizing speckle masking, a classic solar image reconstruction algorithm, this method calculates the atmospheric seeing parameter (r0) using statistical methods. Then, it calculates the modulus and phase from a large number of short-exposure solar speckle images (more than 100 frames) to reconstruct a clear solar image. Its core technique is to reconstruct the modulus and phase of the target image based on the statistical characteristics of the short-exposure speckle images. First, a large number of statistical samples (≥100 frames of short-exposure images) undergo flat-field preprocessing and correlation alignment. Then, the atmospheric seeing parameter (r0) is estimated using the spectral ratio method, and the speckle interferometry transfer function (SITF) is constructed. Next, the preprocessed data is divided into overlapping blocks based on the size of the isohalo region. Based on these blocks, modulus and phase are statistically reconstructed sequentially from the block's statistical samples. The phase of the target image is estimated using the re-spectral method or triple correlation method, i.e., recursively extrapolating from low-frequency phase to high-frequency phase. Finally, the reconstructed sub-blocks are stitched together to obtain the final overall image reconstruction result. However, the disadvantages of the speckle masking method are: (1) The image has artifacts. Since the speckle masking method is based on the triple correlation of short exposure images, it estimates the phase of the target by recursively estimating the phase from the low-frequency phase to the high-frequency phase. In the recursive process, it will inevitably be affected by noise such as photon noise. The noise will accumulate in the high-frequency part, and in severe cases, it will significantly distort the fine structure of the object. When r0 is less than 6cm, the image reconstructed by the speckle masking method contains a large number of artifacts and noisy structures, and can no longer be used normally. (2) SITF deviates from reality. The speckle masking method estimates the atmospheric seeing r0 parameter by the spectral ratio method and calculates the SITF, which is only a theoretical calculation value. Especially after r0 is less than 6cm, the short exposure image has adverse factors such as distortion, deformation and random displacement, which leads to a huge error between SITF and the instantaneous transfer function psf of the optical system of the actual image.

[0005] Technique 2: Multi-Frame Blind Deconvolution (MFBD) is another solar image reconstruction technique. Based on the principle of maximum likelihood estimation, it uses a set of short-exposure solar images to estimate the target image. It has no special requirements for the imaging system and does not require additional physical optical paths. It is the most flexible and effective image post-processing technique in practical applications. Its main core technical means is: The multi-frame blind deconvolution method first inputs multiple frames of short-exposure solar images, then divides the preprocessed data into overlapping blocks according to the size of the isohalo region, and then estimates the wavefront phase coefficient through the optimization algorithm, thereby finding the instantaneous point spread function psf, and using deconvolution to restore the target high-resolution image. However, the disadvantages of multi-frame blind deconvolution are: (1) uncertainty of phase recovery. This technique only relies on the blurred image as the input value and uses the optimization algorithm to find the wavefront phase and target image that are close to the true solution. Mathematically, it is an inverse problem. In the solution process, the target image and wavefront phase coefficient are calculated in reverse by relying on the linear constraints of image degradation. It is easily trapped in local optima due to severe noise, and the calculation results deviate from the actual results. (2) Image distortion was not considered. The problem of severe distortion and random displacement in the speckle image was ignored, which greatly reduced the accuracy of the restored wavefront phase. The calculated PSF was inaccurate, and the restored image could not meet the high resolution requirements by using the deconvolution method.

[0006] Technique 3: The high-resolution solar image reconstruction (NASIR) algorithm based on non-rigid registration is a solar image reconstruction method suitable for fast search and filtering of data. It is the first to use the computational optical flow image method to obtain image phase information. Its main core technology is: the NASIR algorithm uses the optical flow principle in computational vision, and performs pixel-by-pixel displacement field calculation on each frame of solar short exposure image based on the reference frame. The displacement calculation of all short exposure images in the sequence is regarded as one round. Generally, 3-5 rounds of calculation are performed. Finally, the calculated displacement field is used to perform pixel-by-pixel translation to obtain the corrected solar short exposure image. Then, the average calculation is performed, and the average image phase is used as the target image phase. Combined with the speckle masking method, the image modulus is calculated to obtain the reconstructed image result. However, the disadvantages of the high-resolution solar image reconstruction (NASIR) algorithm based on non-rigid registration are: (1) Inaccurate phase. This technique only uses a large number of solar short exposure image samples after non-rigid alignment to obtain the average image and uses the average phase as the phase of the reconstructed image. There is no further accurate estimation of the instantaneous transfer function psf of the system. (2) SITF deviates from reality. The NASIR algorithm also estimates the atmospheric seeing r0 parameter through the spectral ratio method and calculates the SITF. However, the SITF still has an error with the instantaneous transfer function psf of the image optical system, and cannot recover high-frequency image details.

[0007] It is evident that the three closest existing technologies disclosed above all belong to the algorithm category. Although they do not rely on other optical path compensation systems, each method has its limitations in the reconstruction process, resulting in unsatisfactory restored images.

[0008] In view of this, this application aims to address the image reconstruction problems existing in the prior art by proposing a new method for image reconstruction of ground-based solar telescopes, thereby solving the aforementioned problems existing in the current prior art. Summary of the Invention

[0009] To address the aforementioned technical problems, this application aims to provide a method for reconstructing a high-resolution solar image from a short-exposure solar image acquired in normal mode, without relying on any corrective optical path system or other instruments to eliminate the effects of atmospheric turbulence under conditions of poor seeing.

[0010] Based on the analysis of the above-mentioned ground-based solar telescope image reconstruction methods, and combining the principle of wavefront information estimation by image intensity and the non-rigid alignment method, this application proposes a solar image reconstruction technique that combines multi-frame blind deconvolution (MFBD-CNRA) with non-rigid alignment. This algorithm improves upon the wavefront and target image reconstruction based on MFBD. The main contributions are: 1) Considering the distortion and random displacement caused by strong atmospheric turbulence in short-exposure images, a non-rigid alignment technique is used to reasonably correct the geometric shape and structure of the short-exposure image sequence, achieving frame-to-frame registration and alignment; 2) Under weak seeing conditions, for the problem of short-exposure images containing fragmented structures, an improved lucky frame selection method is proposed, selecting lucky images with abundant high-frequency information and stable structures to limit the approximate structural shape of the target and prevent the reconstruction of erroneous structures; 3) Using speckle average frames after non-rigid alignment to supplement the prior knowledge of the target image, initial values ​​of wavefront aberration coefficients are obtained during the optimization process, effectively constraining the confidence interval of the optimization solution and avoiding premature entrapment in local optima; 4) A non-blind deconvolution method is chosen to reconstruct the image, and anisotropic filters are used to effectively smooth and suppress noise, restoring image details.

[0011] Specifically, the solution proposed in this application mainly addresses the following key issues and utilizes new technical approaches to achieve them.

[0012] First: Random displacement and distortion of short-exposure images. When the atmospheric seeing parameter r0 is less than 6cm, random displacement and distortion of solar short-exposure images are corrected by non-rigid alignment; the improved lucky frame selection method mainly serves to eliminate error images, which is beneficial for solving the PSF.

[0013] Second: Solve for the accurate transfer function psf. Initial phase iteration values ​​are obtained using the non-rigidly aligned image. Starting from the initial values, iterate until the accurate phase information is calculated. Then, the actual instantaneous transfer function psf of the system is reconstructed.

[0014] Third: It does not contain artifact structures. Then, through deconvolution, a high-resolution solar image is reconstructed, and the reconstructed image does not contain artifact structures.

[0015] In view of the specific problems to be solved and the technical ideas given above, the specific technical solution of the present invention is as follows:

[0016] More specifically, the first aspect of this invention provides a method for reconstructing images from a ground-based solar telescope under amblyopia conditions, including...

[0017] Acquire short-exposure images of the sun, and perform non-rigid alignment of each frame of short-exposure images of the sun using reference frame images;

[0018] Based on the non-rigidly aligned short-exposure solar images, the improved lucky frame selection method is used to segment the images into blocks and select lucky sub-block images with high structural stability and high frequency.

[0019] An initial phase iteration value is calculated for the selected lucky sub-block image, and the final phase coefficient value is obtained through an optimization algorithm, thereby reconstructing the actual system instantaneous transfer function;

[0020] The sub-block images are reconstructed based on non-blind deconvolution, stitched together, and finally synthesized into a single image.

[0021] As one specific implementation, the non-rigid alignment of each frame of the solar short-exposure image using a reference frame image includes:

[0022] Set an initial reference frame. For each pixel in a set area of ​​a short-exposure image, find the corresponding pixel in the reference frame and obtain the displacement field corresponding to the two pixels.

[0023] By performing reverse displacement and interpolation based on the solved displacement field vector, the distortion displacement of the short exposure image can be restored pixel by pixel.

[0024] As one specific implementation, the non-rigid alignment of each frame of the solar short-exposure image using the reference frame image further includes:

[0025] The reference frame for the next round is set as the average frame of the short exposure image sequence after the previous round of correction. One round is defined as the non-rigid alignment of all the speckle patterns in the sequence once.

[0026] In the above technical solution, the number of iterations of the reference image is selected between 3 and 5 times based on the seeing of the data. The number of iterations can be increased according to the actual seeing situation. After reaching the preset number of correction rounds, the distortion displacement field of each short exposure image is calculated.

[0027] As one specific implementation method, the improved lucky frame selection method includes:

[0028] Based on the frame selection method of speckle interferometry, the average frame of the speckle sequence after non-rigid geometric correction is selected as the reference image, and the structural similarity evaluation index is added.

[0029] The final evaluation criterion is the product of the spectral ratio ring zone integral value and the structural similarity.

[0030] Specifically, the structural similarity evaluation index is as follows:

[0031] ;

[0032] In the formula: It is a short exposure image. The mean, It is the average frame image The mean, It is a short exposure image. variance It is a short exposure image. variance yes and covariance, , It is a constant. It is a range of values ​​at the image pixel level. , .

[0033] Furthermore, the improved frame selection evaluation criterion is expressed by the following formula:

[0034] .

[0035] As a specific implementation method, obtaining the final phase coefficient value through optimization methods and then reconstructing the actual instantaneous transfer function of the system includes:

[0036] Construct a cost function and iteratively solve the cost function starting from the calculated initial phase iteration value.

[0037] When the maximum number of iterations is reached or the result value meets the set error value, the iteration stops and the final phase coefficient value is returned.

[0038] Furthermore, the final phase coefficient value is expressed by the following formula:

[0039] ;

[0040] In the formula: E represents the cost function related to the phase coefficient. Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It refers to the orthogonal polynomial of the th The covariance matrix corresponding to each term has a total of M orthogonal polynomials. These are the Tikhonov regularization parameters for target estimation. These are the Tikhonov regularization parameters for estimating wavefront phase information; the variables are... The goal is to solve for the variables. The cost function E is minimized.

[0041] As one specific implementation, the process of reconstructing sub-block images based on non-blind deconvolution, stitching together the sub-block images, and finally synthesizing the image includes:

[0042] The step of obtaining a smooth filter is to remove all isolated peaks in the filter that cannot be connected to the zero-frequency peak; wherein, the constructed smooth filter has the following form:

[0043] .

[0044] As a specific implementation method, the reconstruction of sub-block images based on non-blind deconvolution, the stitching of sub-block images, and the final synthesis of the image are restored using the following formula:

[0045] ;

[0046] In the formula: Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It is the noise power spectrum estimated outside the selected cutoff frequency. This represents taking the expected value and putting... The value is set to 0.2 to 1, and all values ​​less than 0.2 and greater than 1 are set to 0. H j Refers to the first j Frequency domain function of frame PSF; I j Refer to the input numberj Frequency domain function of a short-exposure image j =1,2,3,4,,,,,10.

[0047] More specifically, a second aspect of the present invention provides a ground-based solar telescope image reconstruction system under poor seeing conditions, comprising:

[0048] The non-rigid alignment module performs non-rigid alignment on each frame of the solar short-exposure image based on the acquired solar short-exposure image and using the reference frame image.

[0049] The filtering module, based on the non-rigidly aligned short-exposure solar images, uses an improved lucky frame selection method to segment and process the images into blocks, selecting lucky sub-block images with high structural stability and high frequency.

[0050] The optimization module calculates an initial phase iteration value for the selected lucky sub-block image and obtains the final phase coefficient value through an optimization algorithm, thereby reconstructing the actual system instantaneous transfer function;

[0051] The restoration module reconstructs sub-block images based on non-blind deconvolution, stitches the sub-block images together, and finally synthesizes the image.

[0052] More specifically, a third aspect of the present invention provides an electronic device, including at least one processor and a memory, characterized in that the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory to implement the steps of the above-described method for reconstructing images of a ground-based solar telescope under weak seeing.

[0053] Compared with the prior art, the present invention has at least the following technical effects:

[0054] 1. A method for reconstructing solar images by combining non-rigid alignment and wavefront phase coefficient calculation.

[0055] This application is the first to propose that solar image reconstruction methods should be considered in two parts: first, a non-rigid alignment method is used to eliminate distortion and random displacement in short-exposure solar images; second, a linear constraint method is used to solve for phase information or the system's instantaneous transfer function (PSF). Combining the advantages of non-rigid registration and phase reconstruction methods, a high-resolution solar image is reconstructed for the first time without any additional optical path systems, provided that the seeing parameter r0 is less than 6 cm.

[0056] 2. Lucky Frame Selection Method

[0057] This application proposes for the first time, based on a frame selection method using speckle interferometry, to use the average frame of the speckle sequence after non-rigid geometric correction as a reference image, and to add a Structural Similarity Indicator (SSIM) as the final evaluation criterion. The product of the spectral ratio annular integral and the structural similarity is used as the final evaluation standard. This effectively selects favorable images with abundant high-frequency information and stable structures to constrain the approximate structural morphology of the target, preventing image reconstruction errors during multi-frame blind deconvolution.

[0058] 3. Solving for the phase coefficient

[0059] The averaged short-exposure solar image after non-rigid alignment is introduced into the target initial term. The phase coefficient value is used as the initial iteration value for the optimization solution process. Iteration is performed, and the iteration stops when the maximum number of iterations is reached or the result value meets the set error value, returning the final phase coefficient value. By setting the initial iteration value, the settling range of the phase coefficient search is greatly constrained, skipping some local optima, thus converging to a more accurate aberration coefficient. Attached Figure Description

[0060] Figure 1 This is a diagram illustrating the overall framework of image reconstruction in this invention.

[0061] Figure 2a The average frame image after cross-correlation and non-rigid alignment of 200 short exposure images.

[0062] Figure 2b A comparison of the power spectrum curves of 200 frames of short exposure images after cross-correlation and non-rigid alignment.

[0063] Figure 3 Reconstructed image of the 12880 active region of the NVST TiO channel 20210930-05:38:42.

[0064] Figure 4 The reconstruction results are from NVST Tio 20201208-03:57:16, with an observation area of ​​12790.

[0065] Figure 5 The power spectrum curve of the reconstructed observation area 12790 is for NVST Tio 20201208-03:57:16.

[0066] Figure 6 Intensity curves for the speckle masking and MBFD-CNRA reconstruction results (pixels at the red line in the speckle masking and MBFD-CNRA reconstruction results).

[0067] Figure 7 The reconstructed image of NVST TiO channel active region 13242, 20230306-06:31:57.

[0068] Figure 8 The power spectrum curve of the reconstructed observation region 13242 is for NVST Tio 20230306-06:31:57.

[0069] Figure 9 Comparison of intensity curves (pixels below the red line) of the reconstruction results from the speckle masking method and MBFD-CNRA.

[0070] Figure 10 Reconstruction results for the observation (active region 12297) of NVST Tio 20230120-03:50:04.

[0071] Figure 11 This represents the average number of frames from the 1st to the 5th non-rigid alignment.

[0072] Figure 12 For comparison of power spectrum curves, (a) power spectrum of the average frame, (b) power spectrum of the 5th frame. Detailed Implementation

[0073] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0074] The background describes three existing techniques that are the main methods for current solar image reconstruction. All are algorithmic and do not rely on additional optical path compensation systems. Their common drawback is that they cannot reconstruct high-quality solar images under conditions of weak seeing.

[0075] The technical solution of this invention is optimized through several modules, including non-rigid alignment, improved lucky frame selection, and phase coefficient solution. The design of each module will be described in detail below.

[0076] Example 1: Complete Design Process (Refer to...) Figure 1-12 )

[0077] I. Non-rigid alignment

[0078] For ground-based solar telescopes, short-exposure images suffer from distortion caused by atmospheric turbulence and random jitter. Traditional methods address this by performing overall image displacement using cross-correlation, but this rigid displacement (where pixels at different locations in the image move by the same amount) only overcomes random jitter and cannot eliminate distortion in different regions of the short-exposure image.

[0079] In computer vision processing, optical flow is often used to establish a model relating light intensity changes to displacement fields. This model is then used for target detection in moving images to obtain the displacement of each pixel of the target across a series of frames, thus deriving the target's spatial trajectory. Non-rigid alignment borrows the principles of optical flow to establish a model relating pixel displacement to intensity changes in short-exposure images.

[0080] However, unlike the consistency of motion between adjacent frames in computer vision processing, adjacent frames in the astronomical field exhibit random jitter and distortion, making it impossible to accurately calculate the displacement field of a short-exposure sequence of images based solely on adjacent frames. Therefore, when using the optical flow method in the MFBD-CNRA computational model, a suitable reference frame image needs to be selected to solve for the optical flow field vectors of the reference frame (Refence Image, RI) and each short-exposure image (Speckle Image) in the short-exposure sequence. This allows for the restoration of distortions in different image regions of the short-exposure image by varying displacement amounts. This pixel-by-pixel "non-rigid" displacement differs from the overall rigid translation of the entire image, providing a reasonable and effective correction of the target's distortion displacement in the spatial domain. Simultaneously, registration between the short-exposure images is completed based on the same reference frame image.

[0081] (1) Selection of the initial reference frame

[0082] Accurate estimation of the displacement field requires a high signal-to-noise ratio image as a reference frame. The reference frame is then used to reconstruct its modulus and phase. Initially, the reference frame is constructed by overlaying short exposure sequences to obtain the average frame image phase. The modulus is then obtained using a statistical reconstruction method based on speckle interferometry. By combining the modulus and phase, a structurally stable reference frame image with high-frequency information is obtained.

[0083] The reconstruction method of the initial reference frame image mode is as follows

[0084] (1)

[0085] In the formula These are spatial frequency domain coordinates. It is a short exposure image. It is an estimate of the noise power spectrum in a short-exposure image. It is the optical transfer function in the theory of ground-based solar telescopes, and it is related to the shape and aperture of the telescope's pupil. It is the theoretical speckle interferometry transfer function (SITF) estimated through seeing. This represents taking the average value.

[0086] (2) Calculation method of displacement field vector

[0087] The pixel intensity distribution in a local area of ​​a short-exposure solar image can be represented as:

[0088] (4)

[0089] In the formula: These are the two-dimensional coordinates of the short-exposure image region. yes Image pixel intensity at the location, It is a symmetric matrix variable. It is a vector. It is a scalar.

[0090] Assume the approximate expression for the pixel intensity distribution of the reference frame is as follows:

[0091] (5)

[0092] When the short exposure image and this region of the reference frame RI have an ideal translation transformation The expression relating pixel intensity and location in this region of the short-exposure image and the reference frame image is as follows:

[0093] (6)

[0094] Set the coefficients to be equal, and solve for...

[0095] (7)

[0096] Therefore, we can establish a computational model for image pixel intensity and translation transformation under ideal conditions. Assuming that the displacement field changes only slowly, we can integrate information within the neighborhood of each pixel. We attempt to find a translation amount in the neighborhood of the image region that best satisfies (7). , It refers to the pixels within the neighborhood. It is a method for calculating the weight of neighboring pixels, where It refers to the first 1 pixel With reference frame vector The difference.

[0097] (8)

[0098] To more accurately describe the motion projection of distortion onto short-exposure images, optimization strategies such as affine transformation of the displacement field and neighborhood pixel weighting can be used to obtain a more reasonable displacement field calculation model. For the projection of general three-dimensional motion onto the image plane, a two-dimensional 8-parameter model is used to represent the displacement field as follows:

[0099] (9)

[0100] Written in matrix form as

[0101] (10)

[0102] (11)

[0103] (12)

[0104] Then there is

[0105] (13)

[0106] When the displacement field changes slowly, the unknowns in the equation are... and In the neighborhood All pixels within the same neighborhood are identical. The equations relating the intensity of multiple pixels in the neighborhood to the translation vector are solved using the least squares method. Then, from equation (10), the translation vector of the short-exposure image pixels in the local area relative to the reference frame pixels can be obtained. This can be extended to the entire image area, thus establishing a distortion displacement field between the short-exposure image and the reference frame.

[0107] (3) Reference image update and iterative alignment

[0108] After setting an initial reference frame, for each pixel in a designated area of ​​each short-exposure image, the corresponding pixel in the reference frame is found. The displacement field corresponding to the two pixels is obtained, and then reverse displacement and interpolation are performed based on the solved displacement field vector to restore the distortion displacement of the short-exposure image pixel by pixel. One non-rigid alignment of all speckle images in the sequence is called one iteration. The reference frame for the next iteration is set to the average frame of the short-exposure image sequence after the previous round of correction, thereby continuously improving the signal-to-noise ratio of the reference image, which is beneficial for more accurate distortion restoration. The number of iterations of the reference image is selected between 3 and 5 times depending on the seeing of the data, and the number of iterations can be increased according to the actual seeing situation.

[0109] After reaching the preset number of correction rounds, the distortion displacement field of each short exposure image is calculated. The original short exposure image is restored pixel by pixel according to the final calculated displacement field, and spatial alignment with the reference frame is completed. The geometry and structure of the short exposure image sequence are reasonably corrected. Figure 1 The image shows the average frame rate obtained after applying cross-correlation alignment and non-rigid alignment to the same set of 200 short-exposure images. Non-rigid alignment improves the average frame rate information and reveals more image detail. To visually compare the frequency domain reconstruction quality, we convert the two-dimensional images into power spectrum curves. Figure 1'a' represents the average frame images of the same group, where (a) indicates the average frame before non-rigid alignment, and (b)-(f) represent the images after the 1st to 5th alignments. Figure 1 b(a) and (f) represent a comparison of the power spectrum curves of 200 frames of short exposure images after cross-correlation and non-rigid alignment. It is clear that non-rigid alignment enhances the mid-to-high frequency energy of the spot pattern to a certain extent.

[0110] II. Improved Lucky Frame Selection Method

[0111] Lucky frame selection refers to selecting images from a sequence of speckle images captured by a ground-based telescope that are less affected by atmospheric turbulence at certain moments. These images retain more high-frequency information and are closer to the true target image. Common frame selection methods rely on parameters such as image intensity or gradient. The lucky frame selection technique used by NVST employs a speckle interferometry-based frame selection strategy. This method uses the integral over the frequency band of the normalized speckle power spectrum as the evaluation criterion to assess the image quality of a sequence of speckle images. The expression for the power spectrum band integral is as follows:

[0112] (14)

[0113] In the formula These are spatial frequency domain coordinates. It refers to the arithmetic mean. It refers to a dot pattern. It refers to high-resolution target images. It is the system's optical transfer function. It is known as the speckle interferometry transfer function. It is the ratio of the square of the average spectrum of the image to the average energy spectrum, and contains only information related to the turbulent atmosphere and the telescope system.

[0114] While frame selection strategies based on speckle interferometry can identify short-exposure images with high-frequency information, they fail to consider the structural fragmentation and deformation caused by rapid atmospheric turbulence. They are not sensitive to image structural stability and cannot effectively remove images containing broken or distorted structures. After non-rigid geometric correction, only the distorted displacement field is restored, failing to repair the content structure of short-exposure images. Therefore, a lucky frame selection method is needed to further select short-exposure images. Selecting lucky images with abundant high-frequency information and stable structures helps limit the approximate structural morphology of the target, preventing errors in image reconstruction during multi-frame blind deconvolution.

[0115] Based on the above research on existing lucky frame selection methods, this application aims to adopt an improved lucky frame selection method or strategy, specifically:

[0116] Based on the frame selection method using speckle interferometry, this paper uses the average frame of the speckle sequence after non-rigid geometric correction as the reference image and adds an overall structural similarity evaluation index. The final evaluation criterion is the product of the spectral ratio annular integral and the structural similarity, which effectively eliminates the aforementioned problems. Structural similarity (SSIM) is an index that measures the similarity between two images. Given a short-exposure image and an average frame image, their structural similarity can be found using the following method:

[0117] (15)

[0118] In the formula It is a short exposure image. The mean, It is the average frame image The mean, It is a short exposure image. variance It is a short exposure image. variance yes and covariance, , It is a constant. It is a range of values ​​at the image pixel level. , The SSIM score ranges from -1 to 1, with a value of 1 when two images are nearly identical.

[0119] The improved frame selection evaluation criteria are

[0120] (16)

[0121] In the formula: δ For power spectrum ratio, the ring band integral is given. SSIM is the structural similarity index, which is a full-reference index calculated based on the mathematical model of the mean, standard deviation and covariance of the images to measure the visual similarity between two images.

[0122] Frames are selected from sub-block images within the same speckle sequence; higher-quality images are ranked higher. Figure 3 As shown, the sub-block images selected by the SI method retain deformed and broken structures, while the sub-block images selected by the improved frame selection method have stable structures and contain high-frequency information. The sub-block images selected by the improved lucky frame selection strategy have less content fragmentation.

[0123] In subsequent experiments, we used the same frame selection strategy for both the multi-frame blind convolution and MFBD-CNRA (multi-frame blind deconvolution) algorithms, selecting 30 frames as input images for each. By comparing the speckle indices of the two frame selection results, we found that occasionally one or two frames had different indices, ensuring that the experimental data were basically consistent.

[0124] III. Wavefront Phase Coefficient Estimation for Multi-Frame Blind Deconvolution

[0125] (1) Principle analysis of optical imaging system

[0126] Under the assumption of equal halo properties, the speckle pattern of the sun in each frame of short exposure is... It can be regarded as the target image And the system's instantaneous transfer function (Point Spread Function, PSF) The convolution of the system; the instantaneous transfer function of the system, abbreviated as psf, is h(x) in the following formula;

[0127] (17)

[0128] It is a two-dimensional coordinate system in image space. This represents the convolution operation. In the frequency domain, the above expression is:

[0129] (18)

[0130] It is the Fourier transform of the PSF, called the system optical transfer function.

[0131] (19)

[0132] In the formula This represents the Fourier operation. It is the Fourier operation rule.

[0133] Assuming the optical system can be represented by a generalized pupil function, Indicates the number of image frames. , This refers to the phase information of each frame of the image. This refers to the amplitude information of each frame of the image, specifying the geometric range of the corresponding pupil, within which... Outside the pupil The generalized pupil function is expressed as:

[0134] (20)

[0135] The goal is to find the final phase coefficient value, where the phase information is unknown. Alternatively, Zernike or KL orthogonal polynomials can be used to describe it. Indicates the chosen orthogonal basis. It is the number of terms in an orthogonal basis. ,use Indicates the first The coefficient corresponding to the term. The phase expression for a short-exposure image is:

[0136] (twenty one)

[0137] The relationship between the system's instantaneous transfer function and the generalized pupil function is as follows:

[0138] (twenty two)

[0139] In the formula This represents the inverse Fourier operation. It refers to the point spread function of the complex amplitude of the system.

[0140] Above, we will After solving, the PSF (Physical Image File) can be obtained. Sub-block segmentation involves taking 256*256 pixel sub-images at equal intervals from a large 2650*2160 pixel image at 100 / 200 frames. Based on these 256*256 sub-images at the same position in the 100 / 200 frames, the most accurate PSF is calculated, thus reconstructing a sub-block image. Sub-block stitching involves reassembling all the reconstructed 256*256 pixel images and stitching them back together in their original positions to form a large 2560*2160 image.

[0141] (2) Construction of the cost function

[0142] Multi-frame blind deconvolution achieves target reconstruction and estimation of the system's instantaneous point spread function or wavefront phase information by establishing an error cost function and finding its minimum value for aberration coefficients and target estimation. Under the principle of maximum likelihood estimation, an error cost function is defined to determine the degree of approximation between the reconstructed target image intensity and the actual acquired blob image intensity.

[0143] (twenty three)

[0144] To further ensure the existence, uniqueness, and continuity of solutions to the blind questionnaire problem during the solution process, Tikhonov regularization terms related to the objective and phase are added to the cost function based on prior information about the objective and phase. The expression of the cost function is as follows:

[0145] (twenty four)

[0146] In the formula These are the Tikhonov regularization parameters for target estimation. These are the Tikhonov canonical parameters used to estimate wavefront phase information. It refers to the orthogonal polynomial of the th The covariance matrix corresponding to each term.

[0147] Therefore, when the target image and the system's instantaneous transfer function are unknown, the problem of estimating wavefront information and the target image from multiple short-exposure images can be transformed into solving the cost generalization function. Regarding variables and phase information The problem of finding the minimum value of the cost function. We can apply nonlinear optimization to solve it, but directly solving for the two unknowns is inefficient and prone to premature convergence.

[0148] (3) Obtain the initial values ​​of wavefront aberration coefficients

[0149] This application adopts a target estimation method. A priori knowledge approach, using non-rigidly corrected averaged short-exposure images Used as the initial prior estimate for target estimation. Alternative target estimation Then, solve for the cost function. Regarding unknown quantities The first-order partial derivative can be solved to obtain...

[0150] (25)

[0151] make Satisfying the following formula

[0152] (26)

[0153] In the formula Regularization parameters , With all the isoparameters known, the other parameters can be represented by the wavefront phase aberration coefficients. Thus, a set of aberration coefficients can be solved. High-resolution images reconstructed from known non-rigid solar images Under the conditions that make Minimum.

[0154] (1) Iterative solution of wavefront aberration coefficients

[0155] To reduce the number of unknowns, solve equation (24) for the target estimation. The partial derivatives of the target are obtained. Regarding the relationship of wavefront phase information, Lofdahl

[14] derived equation (24) for target estimation. The partial derivatives are finally simplified. for (27)

[0156] In the formula: E represents the cost function related to the phase coefficient. Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It refers to the orthogonal polynomial of the th The covariance matrix corresponding to each term has a total of M orthogonal polynomials. These are the Tikhonov regularization parameters for target estimation. These are the Tikhonov regularization parameters for estimating wavefront phase information; the variables are... The goal is to solve for the variables. The cost function E is minimized.

[0157] The phase coefficient value function, the variable is All other quantities are known. Our goal in constructing this formula is to find its minimum value. When this formula converges, we consider the solution to be the phase coefficients we need; that is, we have found a set of final phase coefficients that satisfy this formula. m refers to the m-th phase coefficient. For example, if we have 36 phases, then m = 1, 2, 3, ..., 36. For a complete phase, a1, a, a3, ..., a36 form a set of phase solutions.

[0158] J refers to the frame number. Each image frame corresponds to an am phase coefficient. For example, if 10 frames are input, then the phase can have a... j =1,m=1-36,a j =2,m=1-36,,,,,aj=10,m=1-36.

[0159] At this point, the cost function does not explicitly depend on the objective, so theoretically, an optimization algorithm can be used to find a cost function that satisfies this condition. A set of solutions to the minimum value To estimate wavefront phase information. It is target estimation equal The solution at that time, then As The initial iteration value is used to iterate through formula (26) starting from the initial value. Iteration stops when the maximum number of iterations is reached or the result value meets the set error value, and the final phase coefficient value is returned. By setting the initial iteration value, the final solution process is significantly constrained. The search for the placeability interval skips some local optima, thus converging to a more accurate aberration coefficient. Using formula (22), we obtain the instantaneous point spread function of the telescope.

[0160] (2) Image reconstruction using non-blind deconvolution methods

[0161] In actual observations, solar speckle patterns often contain additional noise. Non-blind deconvolution methods refer to a class of methods that, given the system's point spread function, estimate a clear image from a blurred image even with additional noise. The research focus is on developing appropriate strategies to balance obtaining a clear target image and suppressing noise. Once the system's point spread function is solved using the above steps, we can view the solar image reconstruction process as a non-blind deconvolution method for image reconstruction.

[0162] With added noise, a solar short-exposure speckle pattern can be represented as follows:

[0163] (29)

[0164] In the formula and The power spectrum of a noise-generated image is difficult to obtain accurately in practical problems. Therefore, an approximate ratio is often used to estimate it in specific applications.

[0165] The Tikhonov regularization denoising method employs frequency domain truncation to suppress noise energy amplification caused by the energy attenuation of the point spread function at high frequencies. Its expression is:

[0166] (30)

[0167] When regularization parameter If the selection is inappropriate, it can produce a severe ringing effect, resulting in unclear edges in the restored image. When using Tikhonov regularization and Wiener filtering for denoising, the ratio of noise to signal at different locations is set to the same parameter, which is an isotropic filtering method.

[0168] To better handle noise and image details, this paper constructs a filter in the form of:

[0169] (31)

[0170] In the formula: Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It is the noise power spectrum estimated outside the selected cutoff frequency. This represents taking the expected value and putting... The value of is set to 0.2 to 1, and all values ​​less than 0.2 and greater than 1 are set to 0. This removes all isolated peaks in the filter that cannot be connected to the zero-frequency peak, resulting in a smooth filter. The filter constructs an anisotropic filter by calculating the ratio of noise to signal at different locations, and effectively smooths and suppresses noise.

[0171] (32)

[0172] The above is the complete design process of the technical solution of this invention. The beneficial effects brought about by the above design of this invention are:

[0173] 1. Artifact-free structure

[0174] Unlike the speckle masking method, this technique does not require a recursive process to calculate the image phase, thus avoiding the accumulation of noise errors that could lead to artifact structures in the reconstructed image.

[0175] 2. Lucky Frame Selection

[0176] This technique segments short-exposure solar images after non-rigid alignment into sub-blocks. Through an improved lucky frame selection method, it eliminates some images with severe geometric errors and selects sub-block images with more stable structures and more high-frequency information.

[0177] 3. Accurate phase

[0178] This technique calculates an initial phase iteration value based on the lucky sub-block image, and then uses an optimization method to iteratively solve for the phase starting from the initial phase value. After setting the number of iterations, the accurate phase information is finally calculated. This allows the actual system instantaneous transfer function (PSF) to be reconstructed for each sub-block.

[0179] Example 2: Alternative Scheme for Wavefront Phase Coefficient Estimation in Multi-Frame Blind Deconvolution

[0180] In addition to using optimization methods similar to multi-frame blind deconvolution (MFBD), the phase information can also be solved using the phase difference (PD) algorithm. Compared with the MFBD method, the PD algorithm introduces known aberrations (such as defocus) into the imaging system outside the target focal plane image and then acquires the image, using two (or more) images to eliminate the uncertainty of phase recovery. Lofdahl[7] describes the phase difference method and multi-frame blind deconvolution techniques as problems that solve the wavefront phase coefficients under the linear constraints of the maximum likelihood theory. The phase difference method can be regarded as a special multi-frame blind deconvolution with stronger constraints.

[0181] Example 3: Verification and Analysis of Experimental Results Using Fuxian Lake as an Example

[0182] (1) Table 1 lists the annual average seeing data of Fuxian Lake monitored by the solar differenceimage motion monitor (SDIMM) from 1999 to 2002. r0 is the uncalibrated seeing to the zenith, and r0* is the calibrated seeing to the zenith. r0* can be divided into boundary layer seeing r0B and free atmosphere seeing r0F. The seeing of Fuxian Lake shows a seasonal pattern of good seeing in summer and autumn (May-October) and poor seeing in winter and spring (November-April of the following year). Chen and Liu pointed out that the boundary layer seeing of FSO is very good and has no significant impact on the seasonal variation of overall seeing. The overall seeing of FSO largely depends on the free atmosphere seeing. The reason lies in climatic factors. During the monsoon season (May to October), the subtropical high pressure dominates, and the atmosphere is stable, so the seeing r0F is very good. During the dry season (November to April of the following year), the westerly jet stream dominates, and the upper atmosphere moves quickly, so the seeing r0F in the upper free atmosphere is significantly reduced, resulting in the overall seeing r0 being lower than the annual average.

[0183] The Fuxian Lake Solar Observatory (FSO) experiences more clear days in winter and spring than in summer and autumn, but the average monthly seeing is generally lower, indicating that the seeing distribution at the FSO is not ideal. Given the reduced seeing caused by rapid turbulence in the upper atmosphere, reconstructing high-resolution solar images is an essential task for FSO.

[0184] Table 1. Atmospheric seeing statistics from the Fuxian Lake Solar Observatory

[0185]

[0186] (2) The Fuxian Solar Observatory (FSO) is located in Chengjiang City, Yunnan Province, at 24°N latitude. Located at 34'48"N, 102°57'01"E, with an altitude of 1720 meters, the New Vacuum Solar Telescope (NVST) is a crucial ground-based large-aperture solar telescope in my country. Its primary scientific objective is to conduct high-resolution imaging and spectroscopic observations of the Sun in the 0.3–2.5 micrometer wavelength range, including measuring the fine structure of the Sun's magnetic field and its evolution with high spatiotemporal resolution. The NVST is a horizontal telescope with a vacuum window diameter of 1200 mm, an effective aperture of 980 mm, an effective field of view greater than 3 arcminutes, and a focal length of 45 meters at F3. Its main instruments include a multi-channel high-resolution imaging system, a multi-band spectrometer, a high-dispersion spectrometer, a polarization analyzer, and an adaptive optics system. Currently, the high-resolution imaging system channels in use primarily consist of the chromosphere Halpha (center wavelength 656.26 nm, channel bandwidth 0.025 nm) and the photosphere TiO2 (center wavelength 705.8 nm, channel bandwidth 1 nm). The NVST telescope produces three main types of data: Level 0, which is the raw observation data; Level 1, which is a reconstructed image using frame-shifting stacking after dark field flattening; and Level 1+, which is a high-resolution reconstructed image approaching the diffraction limit using the speckle mask method. Table 2 shows the experimental data, all Level 0 data from the TIO band observed by NVST, covering observation years from 2020 to 2022. Each batch of experimental data consists of 200 short-exposure images, with each frame having an exposure time of approximately 0.15 s. The atmospheric seeing parameters of the experimental data were calculated using the spectral ratio method.

[0187] Table 2 NVST Telescope Experimental Data Information

[0188]

[0189] The reconstruction algorithms include the speckle mask method, the NASIR algorithm, the multi-frame blind resolution algorithm, and the MFBD-CNRA algorithm. We analyze the reconstruction performance of these algorithms by reconstructing high-resolution solar images of the above experimental data.

[0190] (3) Under good seeing conditions

[0191] In summer and autumn, FSO seeing is usually above 10 cm, and the spot occlusion reconstruction effect is better. Figure 3 and Figure 4 The reconstruction results of datasets 1 and 2 are shown, which were reconstructed using speckle masking, MFBD, NASIR, and MFBDCNRA, respectively.

[0192] As can be seen, the images produced by all algorithms clearly display details such as sunspots, solar texture, and solar magnetic field bright spots. From a visual perspective, the reconstruction quality of the four algorithms is quite similar. To intuitively compare the reconstruction quality of the four algorithms in the frequency domain, we convert the two-dimensional power spectrum image to polar coordinates. Then, we take the average value along the polar coordinate angle to obtain a one-dimensional power spectrum. The polar radius length represents the frequency, and the average intensity represents the energy. Figure 4 In the diagram, we plotted the power spectrum of the reconstructed image. In the mid-to-high frequency region, the power spectrum curve is higher than other curves, which is closer to the telescope's limiting resolution. Figure 5 shows the intensity curves of the red-line pixels, further confirming the correctness of the MFBD-CNRA intensity distribution.

[0193] To more accurately describe the quality of image reconstruction, metrics such as SSIM (Symptom Sensitivity to Intensity) and CVoIP (Coefficient of Variation of Intensity Curves) are used to analyze each result. The SSIM index can be used to assess differences between images; it combines three different factors: brightness, contrast, and structure. CVoIP is the ratio of the standard deviation of the intensity curve to its mean, and can be used to measure differences in image contrast.

[0194] Table 3 shows the quantitative comparison results of the speckle mask method with the other three methods. Table 3 shows that the images reconstructed by the speckle mask method have a high correlation and structural similarity with the reconstructed images of NASIR and MFBD-CNRA. Quantitative analysis indicators show that when the line of sight is good, the reconstructed images of NASIR and MFBD-CNRA are close to those of the speckle mask method, while when the line of sight is poor, the reconstructed images of NASIR and MFBD-CNRA even surpass the speckle mask method in image contrast.

[0195] Table 3

[0196]

[0197] (4) When seeing is weak

[0198] As visibility decreases, high-frequency information in short-exposure images is severely lost due to atmospheric effects, and the signal-to-noise ratio begins to decline. Figure 7 The reconstruction results for dataset 5 are shown. As visibility decreases, phase recursion errors gradually accumulate, leading to a decline in reconstruction quality. The gradual accumulation of errors causes the speckle mask method to display false structures, significantly impacting the reconstruction outcome. This has a substantial effect on the reconstructed image.

[0199] MFBD reconstructs local solar textures, but fails to reveal detailed structures such as sunspot outlines, penumbra filaments, and the edges of solar textures. The NASIR algorithm does not contain spurious structures and can display low-frequency information such as solar texture outlines, although it exhibits errors in penumbra reconstruction. The MFBD-CNRA algorithm outperforms other reconstruction algorithms in high-frequency structure representation and preserves true contrast.

[0200] exist Figure 8 In our analysis, we plotted the power spectral profiles of the reconstructed images from dataset 5. The MFBD power spectral profile showed a significant reduction, and the speckle masking method's power spectral profile also decreased rapidly in the high-frequency region. In the mid- and high-frequency regions, the power spectral curves of the NASIR and MFBD-CNRA images were very close and both higher than those of other methods.

[0201] Analysis: The key point of this application is to verify the necessity of non-rigid registration by comparing the reconstruction of observation data by MFBD and MFBDCNRA. Non-rigid registration is a nonlinear constraint for solving the problem of solar image degradation.

[0202] Meanwhile, comparing the results of NASIR and MFBD-CNRA, we found that without a linear constraint optimization solution stage, it is impossible to perfectly reconstruct high-resolution images.

[0203] 1. The role of non-rigid alignment

[0204] To solve the problem of solar image reconstruction, we must consider the influence of the atmosphere on the image. Figure 11 The average frame count of the initial speckle frame sequence is shown, as well as the average frame count of the sequences after the first to fifth registrations. Figure 12 Showing Figure 11 Power spectrum curves of (a) and (f).

[0205] From a geometric perspective, non-rigid registration eliminates the influence of random image displacement caused by atmospheric turbulence, improves pixel registration between corrected image sequences, and is more conducive to overcoming strong turbulence.

[0206] The power spectrum curves show that the corrected reconstructed image exhibits significant enhancement in the mid-to-high frequency range. This helps to bring the resolution of the reconstructed image closer to the diffraction limit of the telescope.

[0207] 2. Indispensable linear constraints

[0208] NASIR offers some improvements in power spectrum, but falls short in image phase because it simply merges the average frame phase and interferometric speckle pattern into the reconstructed image. A drawback of this approach is that the calculated theoretical SITF is identical for the same r0, failing to account for variations in the actual image. MFBD-CNRA solves for phase close to the true value using a linear constraint method.

[0209] The phase, which approximates the true value, is solved using a linear constraint method. For different sets of input images, corresponding PSFs can be calculated. Based on the corrected image and the calculated PSFs, the solution for the reconstructed image will be more satisfactory.

[0210] 3. Improve MFBD-CNRA

[0211] While achieving success, MFBD-CNRA still needs further optimization and improvement in the following aspects:

[0212] 1. Number of iterations. Non-rigid registration based on speckle imaging requires a reference image. It's important to note that the reference image here undergoes approximately 5 iterations; more iterations do not necessarily equate to greater effectiveness. The next optimization strategy should be to establish a reasonable model and select the number of frame iterations based on the value of r0.

[0213] 2. The time efficiency of MFBD-CNRA reconstruction is slower than NASIR, and it does not show significant improvement compared to multi-frame blind devolvation algorithms and speckle masking methods. This is because it still requires processes such as sub-block segmentation, reconstruction, and stitching together large images. We are attempting to optimize the algorithm for high-performance parallel computing to further improve reconstruction efficiency.

[0214] Phase optimization. Phase reconstruction is a challenging problem, and we still use the method of solving for Zernike coefficients to reconstruct the phase. While traditional linear optimization methods are effective, they are not necessarily optimal. Utilizing deep learning to search for phase coefficients is one of the methods we will explore in the future.

[0215] Results: Strong atmospheric turbulence during winter and spring significantly reduced seeing at the Fuxian Lake Solar Observatory, resulting in poor solar image reconstruction using the speckle masking method and the MFBD method. Combining the advantages of non-rigid registration and phase reconstruction methods, we proposed a new solar image reconstruction method—the MFBD-CNRA method—which successfully obtained high-resolution images under strong turbulence conditions.

[0216] The reconstructed images from NVST observation data demonstrate that the MFBD-CNRA algorithm is robust and applicable when the field of view r0 parameter is less than 6 cm.

[0217] Non-rigid registration is a non-linear method to overcome the effects of atmospheric turbulence. Its main function is to register pixels one by one and correct aberrations, thereby preserving more high-frequency information in the target image. Considering the differences in actual images, linear constraints are essential in the accurate PSF calculation stage.

[0218] Therefore, when r0 is less than 6 cm, the distorted image exacerbates the phase recursion error in the speckle mask method, leading to artifact structures. Similarly, the MFBD algorithm gets trapped in local optima when searching for the phase due to the blurring and noise of the input image. Therefore, relying solely on the linear image degradation principle to reconstruct solar images is flawed. To address this issue, we propose the MFBD-CNRA method for solar image reconstruction. We consider atmospheric distortion and use non-rigid registration to correct pixel-level distortion, thus supplementing the nonlinear constraints with image intensity variations. After correcting the short-exposure image, we use a linear method to solve for the wavefront phase to obtain the target image. To verify this idea, we use solar observation data from the NVST telescope to verify the effectiveness of our method compared to other methods. When seeing r0 is around 5 cm, MFBD-CNRA performs better, significantly enhancing the reconstruction of mid- and high-frequency information. This comparative result demonstrates the rationality of the MFBD-CNRA principle—considering both nonlinear and linear constraints in solar image reconstruction. We believe that this method provides a suitable solution for image reconstruction by ground-based solar telescopes under strong turbulent conditions.

[0219] The present invention has been described above with reference to specific embodiments. However, those skilled in the art should understand that these descriptions are exemplary and not intended to limit the scope of protection of the present invention. Those skilled in the art can make various modifications and variations to the present invention based on its spirit and principles, and these modifications and variations are also within the scope of the present invention.

Claims

1. A method for reconstructing images from a ground-based solar telescope under amblyopia, characterized by: include Acquire short-exposure images of the sun, and perform non-rigid alignment of each frame of short-exposure images of the sun using reference frame images; Based on the non-rigidly aligned short-exposure solar images, a modified lucky frame selection method is used to segment sub-blocks and select lucky sub-block images with high structural stability and high frequency. An initial phase iteration value is calculated for the selected lucky sub-block image, and the final phase coefficient value is obtained through an optimization algorithm, thereby reconstructing the actual system instantaneous transfer function; Reconstruct sub-block images based on non-blind deconvolution, stitch the sub-block images together, and finally synthesize the image; The improved lucky frame selection method includes: based on the frame selection method of speckle interferometry, selecting the average frame of the speckle sequence after non-rigid geometric correction as the reference image, and adding a structural similarity evaluation index. The product of the spectral ratio ring zone integral value and the structural similarity is used as the final evaluation criterion; The specific structural similarity evaluation index is as follows: ； In the formula: It is a short exposure image. The mean, It is the average frame image The mean, It is a short exposure image. variance It is a short exposure image. variance yes and covariance, , It is a constant. It is a range of values ​​at the image pixel level. , .

2. The method for reconstructing images from a ground-based solar telescope under weak seeing conditions as described in claim 1, characterized in that: The method of non-rigidly aligning each frame of a short-exposure solar image using a reference frame image includes: Set an initial reference frame. For each pixel in a set area of ​​a short-exposure image, find the corresponding pixel in the reference frame and obtain the displacement field corresponding to the two pixels. By performing reverse displacement and interpolation based on the solved displacement field vector, the distortion displacement of the short exposure image can be restored pixel by pixel.

3. The method for reconstructing images from a ground-based solar telescope under weak seeing conditions as described in claim 2, characterized in that: The improved frame selection evaluation criterion is expressed by the following formula: ； In the formula: δ For power spectrum ratio, the ring band integral is given. SSIM is the structural similarity index, which is a full-reference index calculated based on the mathematical model of the mean, standard deviation and covariance of the images to measure the visual similarity between two images.

4. The method for reconstructing images from a ground-based solar telescope under weak seeing conditions as described in claim 1, characterized in that: The final phase coefficient values ​​are obtained through optimization methods, and the actual instantaneous transfer function of the system is then reconstructed, including: Construct a cost function and iteratively solve the cost function starting from the calculated initial phase iteration value. When the maximum number of iterations is reached or the result value meets the set error value, the iteration stops and the final phase coefficient value is returned.

5. The method for reconstructing images from a ground-based solar telescope under weak seeing conditions as described in claim 4, characterized in that: The final phase coefficient value is expressed by the following formula: ； In the formula: E represents the cost function related to the phase coefficient. Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It refers to the orthogonal polynomial of the th The covariance matrix corresponding to each term has a total of M orthogonal polynomials. These are the Tikhonov regularization parameters for target estimation. The parameters are the Tikhonov regularization terms for estimating wavefront phase information, and the variables are... The goal is to solve for the variables. The cost function E is minimized.

6. The method for reconstructing images from a ground-based solar telescope under weak seeing conditions as described in claim 1, characterized in that: The process of reconstructing sub-block images based on non-blind deconvolution, stitching together the sub-block images, and finally synthesizing the image includes: The step of obtaining a smooth filter is to remove all isolated peaks in the filter that cannot be connected to the zero-frequency peak; wherein, the constructed smooth filter has the following form: ； In the formula: Indicates the number of image frames. I j H represents the intensity of the j-th frame image. j Let represent the optical transfer function of the j-th frame, and * denote the conjugate operator. It is the noise power spectrum estimated outside the selected cutoff frequency. This represents taking the expected value and putting... The value is set to 0.2 to 1, and all values ​​less than 0.2 and greater than 1 are set to 0. H j Refers to the first j Frequency domain function of frame PSF; I j Refer to the input number j Frequency domain function of a short-exposure image j =1,2,3,4,,,10; By removing all isolated peaks from the filter that cannot be connected to the zero-frequency peak, a smooth filter is obtained. The filter constructs the final method for restoring the target by calculating the ratio of noise to signal at different locations: ； In the formula: It refers to high-resolution target images. This represents the inverse Fourier operation.

7. A ground-based solar telescope image reconstruction system under poor seeing conditions, characterized in that: include: The non-rigid alignment module acquires short-exposure solar images and performs non-rigid alignment on each frame of short-exposure solar images using reference frame images. The filtering module, based on the non-rigidly aligned short-exposure solar images, uses an improved lucky frame selection method to segment sub-blocks and filter out lucky sub-block images with high structural stability and high frequency. The optimization module calculates an initial phase iteration value for the selected lucky sub-block image and obtains the final phase coefficient value through an optimization algorithm, thereby reconstructing the actual system instantaneous transfer function; The restoration module reconstructs sub-block images based on non-blind deconvolution, stitches the sub-block images together, and finally synthesizes the image. The improved lucky frame selection method includes: based on the frame selection method of speckle interferometry, selecting the average frame of the speckle sequence after non-rigid geometric correction as the reference image, and adding a structural similarity evaluation index. The product of the spectral ratio ring zone integral value and the structural similarity is used as the final evaluation criterion; The specific structural similarity evaluation index is as follows: ； In the formula: It is a short exposure image The mean, It is the average frame image The mean, It is a short exposure image variance It is a short exposure image variance yes and covariance, , It is a constant. It is a range of values ​​at the image pixel level. , .

8. An electronic device comprising at least one processor and a memory, characterized in that, The memory stores computer instructions, and the processor executes the computer instructions stored in the memory to implement the steps of the ground-based solar telescope image reconstruction method under weak seeing as described in any one of claims 1-6.

Images