A super-resolution imaging method based on deconvolution and full focusing

Abstract

The present invention discloses a super-resolution imaging method based on a total focusing method of deconvolution, which relates to the technical field of super-resolution imaging using the total focusing method. The method specifically comprises the following steps: step 1, performing data acquisition based on a full matrix acquisition mode, and reconstructing an initial image using the total focusing method; step 2, establishing a physical convolution model to describe the blurring effect in the imaging process by analyzing the point spread function of the imaging system; step 3, with the goal of minimizing the imaging error, promoting the generation of non-zero responses only at locations where defects actually exist in the reconstructed image by introducing sparse constraints, thereby suppressing background noise and artifacts. The present invention is based on the traditional total focusing method, integrates the idea of ​​sparse optimization, introduces a point spread function to model the imaging process, and uses a fast iterative threshold method to perform sparse deconvolution on the defect distribution, thereby providing a super-resolution imaging solution for guided wave ultrasonic imaging that has a physical basis, strong robustness, and high computational efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of total focusing method super-resolution imaging, and in particular relates to a total focusing method super-resolution imaging method based on deconvolution. Background Art

[0002] Quality testing of materials and components is crucial in many fields, including industrial production, aerospace, and building structures. Defects can severely impact the safety, reliability, and service life of structures. Therefore, the development of high-precision, high-resolution nondestructive testing technologies has been a research hotspot.

[0003] Ultrasonic array imaging technology is a key tool in nondestructive testing and structural health monitoring. It relies on a multi-channel transducer array to capture internal structural reflections and uses imaging algorithms to reconstruct defect distribution. Common imaging algorithms include Delay-Sum (DAS) and Total Focusing Method (TFM). TFM, based on point-by-point focusing using Full Matrix Capture (FMC) data, offers excellent imaging quality and applicability, making it a mainstream approach in array imaging.

[0004] However, due to limitations in system aperture and operating frequency, the resolution of conventional TFM is still limited by the Rayleigh criterion, making it difficult to accurately identify multiple defects with subwavelength spacing. To overcome this limitation, researchers have attempted to introduce subspace methods such as TR-MUSIC to achieve super-resolution, but these methods are extremely sensitive to noise, and the reconstruction process relies on an accurate estimation of the signal subspace dimensionality.

[0005] Therefore, there is an urgent need for a super-resolution imaging method based on the full focusing method of deconvolution to provide a super-resolution imaging solution for guided wave ultrasound imaging that has a physical basis, strong robustness, and high computational efficiency. Summary of the Invention

[0006] The purpose of the present invention is to provide a super-resolution imaging method based on the total focusing method of deconvolution, which is used to solve the technical problems in the prior art of guided wave ultrasonic imaging, such as difficulty in finding a physical basis, poor robustness and low computational efficiency.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A deconvolution-based all-focusing super-resolution imaging method, comprising:

[0009] Step 1: Data acquisition is performed based on the full matrix acquisition mode, and the initial image reconstruction is performed using the full focusing method;

[0010] Step 2: By analyzing the point spread function of the imaging system, a physical convolution model is established to describe the blurring effect in the imaging process;

[0011] Step 3: With the goal of minimizing imaging errors, sparse constraints are introduced to promote the generation of non-zero responses only at locations where defects actually exist in the reconstructed image, thereby suppressing background noise and artifacts.

[0012] Furthermore, data acquisition is performed based on the full matrix acquisition mode. The specific method is as follows:

[0013] According to the size, shape and expected detection accuracy of the detection area, a limited number of sensors are arranged to cover the entire detection area. Based on all the arranged sensors, an array system containing multiple transducers is built. Narrowband pulses or sine waves modulated by Gaussian envelopes are used as excitation signals. The center frequency is set according to the thickness of the detection object and the target mode. The sampling frequency is greater than or equal to ten times the center frequency. The sampling time window is calculated according to the propagation distance and wave speed. The single excitation-receiving signal is processed by multiple superposition and averaging. High-precision time synchronization technology is used to use each transducer in the array as an excitation source in turn. When a transducer is set as an excitation source, all other transducers are simultaneously used as receiving ends. This operation is performed on each transducer in the array in turn until all transducers have completed the task of acting as an excitation source once, and finally the original full-matrix acquisition data is formed.

[0014] Furthermore, the full focusing method is used to reconstruct the initial image. The specific method is as follows:

[0015] The full focusing method is used to process the original full matrix acquisition data to generate the initial defect image. According to the propagation path between the exciter and the receiver to each pixel point in the imaging area, combined with the group velocity of the Lamb wave in the material and the defect position coordinates, when the position of the defect is aligned with the focus, the array element will experience a time delay. Using the formula represents the time delay, where represents the coordinates of the defect location, represents the coordinates of array element i, It represents the group velocity of the Lamb wave in the material. According to the propagation path length from each exciter and receiver in the sensor array to the target pixel point, combined with the propagation velocity of the Lamb wave in the material, the propagation time delay corresponding to each pair of excitation-receiving combinations is calculated. Subsequently, the original discrete sampling signal is interpolated, and the received signal of each pixel point is adjusted according to the calculated propagation time delay. The signals of each channel are aligned by delay and amplitude accumulation or energy accumulation is performed. The amplitude of each channel at the delay point is squared and then accumulated, which is equivalent to the accumulated energy response. The accumulated result is amplitude normalized, or the defect signal is highlighted by dynamic range limitation, and background stray noise is suppressed to complete the focusing of the wave field information.

[0016] Furthermore, by analyzing the point spread function of the imaging system, a physical convolution model is established to describe the blur effect in the imaging process. The specific method is as follows:

[0017] In experimental or simulation data, the distance between the center of the scatterer and the nearest other scatterers is set to d. When the distance satisfies d≥2PSF, the scatterer is judged to be isolated. The amplitude of the scatterer center is set to a. When the amplitude satisfies a≥3bac, the scatterer is judged to be intense. An isolated and intense single scattered echo area is selected, and a small imaging sub-area around the center of the area is intercepted with the origin. The amplitude or energy distribution in the sub-area is directly used as the numerical expression of the point spread. Based on the array geometric parameters, wave velocity information and excitation signal characteristics, the spatial response function of the system is theoretically derived to obtain the expected point spread function pattern. The point spread function is fitted with a two-dimensional Gaussian distribution or Airy disk function. The PSF matrix obtained by the fitting formula is the complete response model of the imaging system for the point source. A convolution relationship is established between the PSF and the actual observed image.

[0018] Furthermore, a two-dimensional Gaussian distribution or Airy disk function is used to fit the point spread function. The specific method is as follows:

[0019] Using the formula The point spread function is fitted, where represents the coordinates of the center of the isolated point scatterer, A is the amplitude normalization constant, Indicates the control of diffusion width, Represents the spatial coordinates of the local coordinate system plane established with the center of the isolated point scatterer as the origin.

[0020] Furthermore, with the goal of minimizing the imaging error, a sparse constraint is introduced to promote the generation of non-zero responses in the reconstructed image only at the locations where defects actually exist. The specific method is as follows:

[0021] The blurred image generated by the initial full focus is regarded as the result of the convolution of the true defect distribution and the system point spread function, and noise interference is superimposed. The objective function is constructed with the goal of minimizing the imaging error. The sparsity constraint is introduced, that is, the absolute values ​​of all pixel amplitudes are summed, and the sparsity term is added to the total objective function. The point source localization deconvolution algorithm based on the accelerated gradient projection method is obtained, which is denoted as the fast iterative shrinkage threshold algorithm. Based on the current estimated defect image, the gradient direction of the convolution error is calculated, and iterative updates with step size control are performed along the gradient direction to reduce the reconstruction error. A shrinkage operation is applied to the updated image to suppress small amplitude noise to zero and retain only significant defect responses. A momentum acceleration mechanism is introduced to improve the convergence speed. After several iterations, the reconstruction error converges to the preset threshold or the maximum number of iterations is reached, and the final high-resolution defect image is output.

[0022] Furthermore, with the goal of minimizing the imaging error, an objective function is constructed. The specific method is as follows:

[0023] Using the formula represents the objective function, where represents target imaging, represents the image generated by the original data, represents the 2D Fourier transform, represents the 2D inverse Fourier transform, represents the Hadamard product, D is the first-order difference matrix, Represents a non-negative constraint, using the formula represents, and λ represents the weight parameter of the sparse regularization term.

[0024] Furthermore, a fast iterative shrinkage threshold algorithm is used. The specific method is as follows:

[0025] Using the formula represents a fast iterative shrinkage threshold algorithm, where is the data consistency item, is the sparse regularization term. The weight parameter λ of the sparse regularization term is used to make a trade-off between imaging error and sparsity requirements, balancing reconstruction accuracy and sparsity. FISTA approaches the optimal solution by combining shrinkage threshold operation and momentum acceleration after each gradient descent step.

[0026] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0027] 1. This invention extracts the diffusion effects of array aperture, propagation mode, and system bandwidth on imaging through the imaging response of isolated point scatterers, establishes a PSF physical convolution model, and provides a mathematical basis for super-resolution reconstruction. It uses a two-dimensional Gaussian distribution or Airy disk function to fit the PSF, accurately describing the spatial response of the system, and solving the problem of difficult quantification of blurring effects in traditional methods.

[0028] 2. The present invention models the TFM blurred image as the convolution and superposition noise of the real defect and the PSF, constructs the objective function through the least squares criterion, and realizes the quantitative optimization of the imaging error. By introducing the first-order difference matrix to constrain the spatial smoothness, excessive oscillation of the reconstructed image is avoided, and the accuracy of defect positioning is improved. Through sparse regularization, only significant defect responses are retained, background noise and artifacts are suppressed, and spatial sparsity of the defect image is achieved. By combining the FISTA algorithm with momentum acceleration and soft threshold processing, the iteration speed is improved compared with the traditional gradient descent method while maintaining sparsity, thereby shortening the calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0030] Figure 1 A step diagram of a super-resolution imaging method based on deconvolution and full focusing method is shown;

[0031] Figure 2 A schematic diagram of the Lamb wave group velocity dispersion curve in the present invention is shown;

[0032] Figure 3 A schematic diagram of verifying the implementation results of the present invention is shown. DETAILED DESCRIPTION

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0034] like Figure 1 、 Figure 2 、 Figure 3 As shown, a super-resolution imaging method based on the deconvolution method includes the following steps:

[0035] Step 1: Data acquisition is performed based on the full matrix acquisition mode, and the initial image reconstruction is performed using the full focusing method.

[0036] Based on the size and shape of the inspection area and the expected inspection accuracy, a limited number of sensors are deployed to ensure that they can cover the entire inspection area. Based on all the deployed sensors, an array system containing multiple transducers is constructed. A narrowband pulse or a sine wave modulated with a Gaussian envelope is used as the excitation signal. The center frequency is set in the range of 100–500 kHz based on the thickness of the inspection object and the target mode (such as A0 or S0 mode). The sampling frequency is greater than or equal to ten times the center frequency. The sampling time window is calculated based on the propagation distance and wave velocity. A single excitation-received signal is processed by multiple superposition and averaging to improve the signal-to-noise ratio. High-precision time synchronization technology, such as GPS synchronization or atomic clock synchronization, is used to accurately synchronize the excitation and reception time of each transducer. Each transducer in the array is sequentially used as an excitation source. When a transducer is set as an excitation source, all other transducers are simultaneously used as receivers. The excitation source transducer sends a signal, and the receiver transducer records the reflected signal. This process is repeated for each transducer in the array until all transducers have completed their task as an excitation source, ultimately forming the original full-matrix acquisition data.

[0037] After data acquisition is completed, the raw full-matrix capture (FMC) data is processed using the total focusing method to generate the initial defect image. Based on the propagation path between the exciter and the receiver to each pixel in the imaging area, combined with the group velocity of the Lamb wave in the material and the coordinates of the defect position, when the position of the defect is aligned with the focus, the array element will experience a time delay. The formula relative to the focus distance is as follows:

[0038] ;

[0039] in, represents the coordinates of the defect location, represents the coordinates of array element i, The group velocity of the Lamb wave in the material is obtained from the theoretical value of the dispersion curve. Based on the propagation path length from each exciter and receiver in the sensor array to the target pixel, combined with the propagation velocity of the Lamb wave in the material, the propagation time delay corresponding to each excitation-receiving pair is calculated. The time delay is obtained by dividing the geometric path by the wave velocity.

[0040] Subsequently, the original discrete sampling signal is interpolated with high precision (such as using linear interpolation, cubic spline interpolation, or sinc interpolation). For each pixel, the received signal is adjusted according to the calculated propagation time delay. The signals of each channel are aligned by delay and amplitude accumulation or energy accumulation is performed. For example, if the propagation time delay of a channel is calculated to be Δt, the signal of that channel is shifted to the right by Δt (if Δt is positive) or to the left by |Δt| (if Δt is negative) on the time axis. The instantaneous amplitude of each channel after delay alignment is extracted and then directly added to obtain the amplitude response of the pixel. The amplitude of each channel at the delay point is squared and then accumulated, which is equivalent to the accumulated energy response. The accumulated result is amplitude normalized, or dynamic range limitation is used to highlight defect signals and suppress background stray noise, thereby completing the focusing of wavefield information.

[0041] Step 2: By analyzing the point spread function of the imaging system, a physical convolution model is established to describe the blurring effect in the imaging process.

[0042] By analyzing the response of an isolated point scatterer in the imaging area (such as a tiny artificially introduced reflection source or a preset reference defect in a defect-free area) in the TFM imaging results, the spatial expansion of the point scatterer under the imaging system is obtained. The isolated point response exhibits energy diffusion characteristics due to the influence of the array aperture, propagation mode, and system bandwidth during the imaging process. By extracting this characteristic, the point spread function of the imaging system is obtained. The specific method includes:

[0043] In experimental or simulation data, the distance between the center of the scatterer and the nearest other scatterer is set to d. When the distance satisfies d ≥ 2PSF, the scatterer is judged to meet the isolation property. PSF is the theoretical resolution of the system (such as the half-maximum width FWHM). Ensure that there are no interference sources around the target scatterer. Set the amplitude of the scatterer center to a. When the amplitude satisfies a ≥ 3bac, the scatterer is judged to meet the intensity property.

[0044] An isolated and intense single scattered echo region is selected. A small imaging sub-region is captured around the center of the region as the origin. The amplitude or energy distribution within the sub-region is directly used as the numerical expression of the point spread. Based on the array geometric parameters (such as sensor spacing and aperture size), wave velocity information such as the group velocity of each Lamb wave mode), and the excitation signal characteristics (center frequency and bandwidth), the spatial response function of the system is theoretically derived to obtain the expected point spread function pattern. The point spread function is then fitted using a two-dimensional Gaussian distribution or Airy disk function:

[0045] ;

[0046] in, represents the coordinates of the center of the isolated point scatterer, A is the amplitude normalization constant, Indicates the control of diffusion width, Represents the spatial coordinates of the local coordinate system plane established with the center of the isolated point scatterer as the origin.

[0047] The PSF matrix obtained by fitting the formula is the complete response model of the imaging system for point sources. By establishing a convolution relationship between the PSF and the actual observed image, the diffusion blur effect in the imaging process can be effectively described, providing a physical basis and calculation basis for the subsequent sparse deconvolution solution of the defect image.

[0048] Step 3: With the goal of minimizing imaging errors, sparse constraints are introduced to promote the generation of non-zero responses only at locations where defects actually exist in the reconstructed image, thereby suppressing background noise and artifacts.

[0049] The blurred image generated by the initial total focusing method (TFM) is considered to be the result of the convolution of the actual defect distribution and the system point spread function (PSF). Noise interference is superimposed, and the objective function is constructed with the goal of minimizing the imaging error. This objective function is used to measure the difference between the current estimated defect image after PSF convolution and the observed blurred TFM image. The imaging error adopts the least squares criterion, that is, minimizing the Euclidean distance between the predicted image and the observed image. The specific formula of the objective function is as follows:

[0050] ;

[0051] in, represents target imaging, represents the image generated by the original data, represents the 2D Fourier transform, represents the 2D inverse Fourier transform, represents the Hadamard product, D is the first-order difference matrix, Represents a non-negative constraint, using the formula represents, and λ represents the weight parameter of the sparse regularization term.

[0052] In order to make the reconstructed image spatially sparse, that is, most pixel values ​​are close to zero and responses are only generated at the locations where defects actually exist, the present invention introduces a sparsity constraint, that is, summing the absolute values ​​of all pixel amplitudes and adding this sparsity term to the overall objective function. This results in a point source localization deconvolution algorithm based on the accelerated gradient projection method, denoted as the fast iterative shrinkage threshold algorithm (FISTA). The specific formula of FISTA is:

[0053] ;

[0054] in, is the data consistency item, is a sparse regularization term. The weight parameter λ of the sparse regularization term is used to make a trade-off between imaging error and sparsity requirements, balancing reconstruction accuracy and sparsity. The weight value can be set based on the actual noise level or defect size experience, and can also be optimized through methods such as cross-validation. FISTA can quickly approach the optimal solution while maintaining the sparsity characteristics by combining the shrinkage threshold operation and momentum acceleration after each gradient descent step.

[0055] The specific implementation steps of FISTA are as follows: based on the current estimated defect image, the gradient direction of the convolution error is calculated, and iterative updates with step size control are performed along the gradient direction to reduce the reconstruction error. A shrinkage operation (i.e., soft threshold processing) is applied to the updated image to suppress small-amplitude noise to zero, retaining only significant defect responses. A momentum acceleration mechanism is introduced so that each iteration not only depends on the current step size but also combines the information of the previous iteration to improve the convergence speed. After several iterations, until the reconstruction error converges to the preset threshold or reaches the maximum number of iterations, the final high-resolution defect image is output.

[0056] Through this sparse deconvolution process, the blur and noise interference caused by the system diffusion effect can be effectively removed, and the defect image close to the actual distribution can be restored, thereby achieving super-resolution imaging beyond the diffraction limit.

[0057] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

[0058] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to specific embodiments. Obviously, many modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A super-resolution imaging method based on deconvolution and full focusing method, characterized in that: include: Step 1: Data acquisition is performed based on the full matrix acquisition mode, and the initial image reconstruction is performed using the full focusing method; Step 2: By analyzing the point spread function of the imaging system, a physical convolution model is established to describe the blurring effect in the imaging process; In experimental or simulation data, the distance between the center of the scatterer and the nearest other scatterers is set to d. When the distance satisfies d ≥ 2PSF, the scatterer is judged to be isolated. PSF is the theoretical resolution of the system. The amplitude of the scatterer center is set to a. When the amplitude satisfies a ≥ 3bac, the scatterer is judged to be strong. An isolated and strong single scattered echo area is selected. The center of the area is taken as the origin, and a small imaging sub-area around it is intercepted. The amplitude or energy distribution in the sub-area is directly used as the numerical expression of the point spread. Based on the array geometric parameters, wave velocity information and excitation signal characteristics, the spatial response function of the system is theoretically derived to obtain the expected point spread function pattern. The point spread function is fitted using a two-dimensional Gaussian distribution or Airy disk function. The PSF matrix obtained by the fitting formula is the complete response model of the imaging system for the point source. Step 3: With the goal of minimizing imaging errors, sparse constraints are introduced to promote the generation of non-zero responses only at locations where defects actually exist in the reconstructed image, thereby suppressing background noise and artifacts.

2. The method of claim 1, wherein the method comprises: Data acquisition is performed based on the full matrix acquisition mode. The specific method is as follows: According to the size, shape and expected detection accuracy of the detection area, a limited number of sensors are arranged to cover the entire detection area. Based on all the arranged sensors, an array system containing multiple transducers is built. Narrowband pulses or sine waves modulated by Gaussian envelopes are used as excitation signals. The center frequency is set according to the thickness of the detection object and the target mode. The sampling frequency is greater than or equal to ten times the center frequency. The sampling time window is calculated according to the propagation distance and wave speed. The single excitation-receiving signal is processed by multiple superposition and averaging. High-precision time synchronization technology is used to use each transducer in the array as an excitation source in turn. When a transducer is set as an excitation source, all other transducers are simultaneously used as receiving ends. This operation is performed on each transducer in the array in turn until all transducers have completed the task of acting as an excitation source once, and finally the original full-matrix acquisition data is formed.

3. The method for super-resolution imaging based on deconvolution and total focusing method according to claim 1, wherein: The full focusing method is used to reconstruct the initial image. The specific method is as follows: The full focusing method is used to process the original full matrix acquisition data to generate the initial defect image. According to the propagation path between the exciter and the receiver to each pixel point in the imaging area, combined with the group velocity of the Lamb wave in the material and the defect position coordinates, when the position of the defect is aligned with the focus, the array element will experience a time delay. Using the formula represents the time delay, where represents the coordinates of the defect location, represents the coordinates of array element i, It represents the group velocity of the Lamb wave in the material. According to the propagation path length from each exciter and receiver in the sensor array to the target pixel point, combined with the propagation velocity of the Lamb wave in the material, the propagation time delay corresponding to each pair of excitation-receiving combinations is calculated. Subsequently, the original discrete sampling signal is interpolated, and the received signal of each pixel point is adjusted according to the calculated propagation time delay. The signals of each channel are aligned by delay and amplitude accumulation or energy accumulation is performed. The amplitude of each channel at the delay point is squared and then accumulated, which is equivalent to the accumulated energy response. The accumulated result is amplitude normalized, or the defect signal is highlighted by dynamic range limitation, and background stray noise is suppressed to complete the focusing of the wave field information.

4. The method of claim 1, wherein the method comprises: The point spread function is fitted using a two-dimensional Gaussian distribution or Airy disk function. The specific method is as follows: Using the formula The point spread function is fitted, where represents the coordinates of the center of the isolated point scatterer, A is the amplitude normalization constant, Indicates the control of diffusion width, Represents the spatial coordinates of the local coordinate system plane established with the center of the isolated point scatterer as the origin.

5. The method of super-resolution imaging based on deconvolution and total focusing method according to claim 1, characterized in that: With the goal of minimizing the imaging error, a sparse constraint is introduced to promote the generation of non-zero responses in the reconstructed image only at the locations where defects actually exist. The specific method is as follows: The blurred image generated by the initial full focus is regarded as the result of the convolution of the true defect distribution and the system point spread function, and noise interference is superimposed. The objective function is constructed with the goal of minimizing the imaging error. The sparsity constraint is introduced, that is, the absolute values ​​of all pixel amplitudes are summed, and the sum is recorded as a sparse term. The sparse term is added to the overall objective function, and a point source localization deconvolution algorithm based on the accelerated gradient projection method is obtained, which is recorded as a fast iterative shrinkage threshold algorithm. Based on the current estimated defect image, the gradient direction of the convolution error is calculated, and iterative updates with step size control are performed along the gradient direction to reduce the reconstruction error. A shrinkage operation is applied to the updated image to suppress small-amplitude noise to zero, retaining only significant defect responses. A momentum acceleration mechanism is introduced to improve the convergence speed. After several iterations, the reconstruction error converges to the preset threshold or the maximum number of iterations is reached, and the final high-resolution defect image is output.

6. The method of super-resolution imaging based on deconvolution and total focusing method according to claim 5, characterized in that: With the goal of minimizing the imaging error, the objective function is constructed. The specific method is as follows: Using the formula represents the objective function, where represents target imaging, represents the image generated by the original data, represents the 2D Fourier transform, represents the 2D inverse Fourier transform, represents the Hadamard product, D is the first-order difference matrix, Represents a non-negative constraint, using the formula represents, and λ represents the weight parameter of the sparse regularization term.

7. The method of super-resolution imaging based on deconvolution and total focusing method according to claim 5, characterized in that: Fast iterative shrinkage threshold algorithm, the specific method is: Using the formula represents a fast iterative shrinkage threshold algorithm, where is the data consistency item, is the sparse regularization term. The weight parameter λ of the sparse regularization term is used to make a trade-off between imaging error and sparsity requirements, balancing reconstruction accuracy and sparsity. The fast iterative shrinkage threshold algorithm approaches the optimal solution by combining the shrinkage threshold operation with momentum acceleration after each gradient descent step.

Images