Super-resolution image reconstruction method based on photon integrated interferometry imaging

Abstract

The present invention relates to the technical field of photon integrated interference imaging, and in particular to a super-resolution image reconstruction method of photon integrated interference imaging, comprising: S1: calculating the frequency sampling points of the photon integrated interference imaging system under non-uniform sparse sampling; S2: obtaining the frequency sampling points of the zero-filled image spectrum; S3: initializing the zero-filled image spectrum using the zero-filled spectrum mask; S4: obtaining the spatial domain zero-filled image; S5: constructing the zero-filled image mask; S6: obtaining the reconstruction target function after zero-filling; S7: converting the reconstruction target function after zero-filling to the spatial domain for solving; S8: solving the augmented Lagrange multiplier function using the alternating multiplier method; S9: obtaining the super-resolution reconstructed image. The present invention can effectively overcome the coordinate approximation error and artifact problems caused by non-uniform sparse sampling, and improve the signal-to-noise ratio of the reconstructed image.

Description

Technical Field

[0001] The invention belongs to the technical field of photon integrated interference imaging, and in particular relates to a super-resolution image reconstruction method of photon integrated interference imaging. Background Art

[0002] The photon integrated interference system is based on the Van Sitzennik theorem. It obtains the fringe complex visibility through the interference baseline formed by two sub-apertures, thereby obtaining the Fourier spectrum information of the target. High-density frequency sampling (uv coverage) can be achieved by gradually changing the length and direction of the baseline. The target image can be obtained by performing an inverse Fourier transform on the uv coverage spectrum formed by the acquired frequency information. However, unlike the target continuous frequency signal obtained by the traditional optical system, the sampling of the photon integrated interference system is sparse and non-uniform sampling, which cannot achieve full coverage of the spectrum information, resulting in poor image reconstruction quality of photon integrated interference imaging, more artifacts in the image, and low signal-to-noise ratio. Summary of the invention

[0003] In view of this, the present invention aims to provide a super-resolution image reconstruction method of photon integrated interferometry imaging to solve the problem of low resolution and low signal-to-noise ratio of the reconstructed image due to the shortcomings of non-uniform sparse sampling such as acquisition frequency redundancy, approximate error and frequency missing.

[0004] A super-resolution image reconstruction method for photon integrated interference imaging specifically comprises the following steps:

[0005] S1: According to the baseline configuration and baseline pairing method of the photon integrated interferometric imaging system, the frequency sampling points of the photon integrated interferometric imaging system under non-uniform sparse sampling are calculated;

[0006] S2: Calculate the reconstructed image The size of the image will be reconstructed Fill zero N times to obtain the frequency sampling points of the zero-filled image spectrum;

[0007] S3: Generate a zero-padded spectrum mask using the frequency sampling points of the zero-padded image spectrum, and initialize the zero-padded image spectrum S using the zero-padded spectrum mask;

[0008] S4: Inverse Fourier transform of the initialized zero-padded image spectrum into the spatial domain to obtain the initialized zero-padded image ;

[0009] S5: construct a zero-filled image mask, and replace the zero-filled image mask with the reconstructed image The value of the area corresponding to the distribution area of ​​​​the reconstructed image is set to 1, and the zero-filled image mask that does not correspond to the reconstructed image The value of the area corresponding to the distribution area is set to 0;

[0010] S6: construct a spatial domain zero-padded image, and introduce the spatial domain zero-padded image gradient into the reconstruction objective function to obtain the reconstruction objective function after zero-padded;

[0011] S7: The reconstructed objective function after zero padding is converted to the spatial domain for solution by the following formula:

[0012] (1);

[0013] (2);

[0014] (3);

[0015] (4);

[0016] in, Ψ is the spectrum of the spatial zero-filled image, w is the spatial domain zero-filled image gradient, is the penalty coefficient, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the anisotropic or isotropic TV regularization term, is the inverse Fourier transform, To initialize the zero-padded image, Zero-fill image in the spatial domain;

[0017] S8: Convert equations (1) to (4) into augmented Lagrange multiplier function formulas, and use the alternating multiplier method to solve the augmented Lagrange multiplier function to obtain the reconstructed zero-filled image;

[0018] S9: Use the zero-filled image mask to reconstruct the corresponding reconstructed image in the zero-filled image The target area is taken out to obtain a super-resolution reconstructed image.

[0019] Furthermore, in step S1, the calculation formula of the frequency sampling points of the photon integrated interference imaging system under non-uniform sparse sampling is:

[0020] (5);

[0021] in,( , ) is the spatial coordinate of the p-th pairing baseline, is the jth imaging wavelength of the photon integrated interferometric imaging system, z is the imaging distance of the photon integrated interferometric imaging system, are the coordinates of the frequency sampling points of the photon integrated interferometric imaging system, and there are n groups of frequency sampling points in total.

[0022] Furthermore, in step S2, the image is reconstructed The calculation formula for the size is:

[0023] (6);

[0024] (7);

[0025] (8);

[0026] (9);

[0027] Among them, m is the size of the super-resolution reconstructed image, R is the number rounded up, is the ratio of the maximum frequency to the fundamental frequency of the photon integrated interferometric imaging system, is the maximum frequency of the photon integrated interferometric imaging system, is the fundamental frequency of the photon integrated interferometric imaging system, N is the zero-filling ratio, B min is the shortest paired baseline, B max is the longest paired baseline, is the minimum imaging wavelength of the photon integrated interferometric imaging system, is the maximum imaging wavelength of the photon integrated interferometric imaging system, and z is the imaging distance of the photon integrated interferometric imaging system.

[0028] Furthermore, in step S3, the calculation formula of the zero-filled spectrum mask is:

[0029] (10);

[0030] (11);

[0031] (12);

[0032] in, is the coordinate of the nth group of frequency sampling points, N is the frequency sampling points expanded N times, P is the zero-filled spectrum mask, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

[0033] Furthermore, in step S3, the formula for initializing the zero-padded image spectrum using the zero-padded spectrum mask is:

[0034] (13);

[0035] in, is the initialized zero-filled image spectrum, is the complex visibility of the nth group of frequency sampling points, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

[0036] Furthermore, in step S4, the formula for inverse Fourier transform of the initialized zero-filled image spectrum to the spatial domain is:

[0037] (14);

[0038] Among them, F -1 is the inverse Fourier transform, Initialize the zero-filled image The coordinates of is the initialized zero-padded image spectrum.

[0039] Furthermore, in step S5, the formula of the zero-filled image mask is:

[0040] (15);

[0041] Where M is the value of the zero-filled image mask, Initialize the zero-filled image , m is the size of the super-resolution reconstructed image, and N is the zero padding factor.

[0042] Furthermore, step S6 specifically includes the following steps:

[0043] S61: construct a spatial domain zero-filled image, and establish a reconstruction objective function based on the spatial domain zero-filled image and the reconstructed image:

[0044] (16);

[0045] (17);

[0046] (18);

[0047] in, is the zero-filling operation, P is the zero-filling spectrum mask, Ψ is the spectrum of the spatial zero-filled image, To initialize the zero-filled image spectrum, is the Fourier transform, x is the spatial domain zero-filled image, To reconstruct the image, is the fidelity term of the objective function;

[0048] S62: Introduce the spatial domain zero-filled image gradient into the reconstruction objective function through the following formula to obtain the reconstruction objective function after zero-filling:

[0049] (19);

[0050] Where P is the zero-filled spectrum mask, Ψ is the spectrum of the spatial domain zero-padded image, S is the spectrum of the initialized zero-padded image, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the inverse Fourier transform, is the Fourier transform, To reconstruct the image, For zero padding operation, w is the spatial domain zero-filled image gradient, is the penalty coefficient, || w ||1 represents anisotropic or isotropic TV regularization terms, and x is a zero-padded image in the spatial domain.

[0051] Further, in step S8, the Lagrange multiplier function is augmented The function expression is:

[0052] (20);

[0053] in, and is the Lagrange multiplier term, w is the spatial domain zero-filled image gradient, is the spatial zero-filled image, Ψ is the spectrum of the spatial zero-filled image, , and is the penalty coefficient, To initialize the zero-padded image, is the Fourier transform, is the inverse Fourier transform, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, and P is the zero-filled spectrum mask.

[0054] Furthermore, step S8 specifically includes the following steps:

[0055] S81: Assume Ψ, w , , The initial value of is 0, and the spatial domain is filled with zero images , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w The number of image rows and columns are both e and f, and the image is filled with zeros in the space domain. , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w As sub-problems of augmented Lagrange multiplier functions, the expressions of the three sub-problems are as follows:

[0056] (twenty one);

[0057] (twenty two);

[0058] (twenty three);

[0059] Where k is the number of iterations;

[0060] S82: Iteratively solve equations (21) to (23), and use the augmented Lagrange multiplier function to solve ,Ψ, w Take the derivative and get the updated , , The solution value of ;

[0061] S83: Repeat steps S81-S82 until k=100 or ( x k+1 - x k ) 2 / m / m<0.001, and the reconstructed zero-filled image is obtained.

[0062] Compared with the prior art, the invention can achieve the following beneficial effects:

[0063] The present invention creates the super-resolution image reconstruction method of photon integrated interference imaging, which implements zero-filling operation by amplifying the coordinate values ​​of frequency sampling points, and solves the problems of sampling frequency redundancy and decreased quality of reconstructed images caused by frequency approximation errors under traditional discrete Fourier transforms. On the one hand, the present invention accurately solves the gradient of the reconstructed image of non-uniform sparse sampling, overcoming the difficulty that the gradient cannot be solved under the premise of non-uniform sampling. On the other hand, the present invention helps accelerate the convergence of the reconstruction process by constraining the zero-filling area with zero gradient, and can effectively overcome the coordinate approximation error and artifact problems caused by non-uniform sparse sampling, thereby improving the signal-to-noise ratio of the reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0065] Figure 1 A schematic flow chart of a super-resolution image reconstruction method of photon integrated interference imaging according to an embodiment of the present invention;

[0066] Figure 2 A schematic diagram of the distribution of frequency sampling points according to an embodiment of the present invention;

[0067] Figure 3 A schematic diagram of the structure of the spatial domain mask described in the embodiment of the present invention;

[0068] Figure 4 To create a simulated high-resolution image as described in the embodiment of the present invention;

[0069] Figure 5 The reconstructed image obtained by using the conventional photon integrated interference imaging technology described in the embodiment of the present invention;

[0070] Figure 6 The super-resolution reconstructed image is obtained by the super-resolution image reconstruction method of photon integrated interference imaging described in the embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0072] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0073] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0074] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0075] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0076] like Figure 1-Figure 3 As shown, the super-resolution image reconstruction method of photon integrated interference imaging provided by the embodiment of the present invention specifically includes the following steps:

[0077] S1: According to the baseline configuration and baseline pairing method of the photon integrated interferometric imaging system, the frequency sampling points of the photon integrated interferometric imaging system under non-uniform sparse sampling are calculated.

[0078] The calculation formula of the frequency sampling point of the photon integrated interferometric imaging system under non-uniform sparse sampling is:

[0079] (1);

[0080] in,( , ) is the spatial coordinate of the p-th pairing baseline, is the jth imaging wavelength of the photon integrated interferometric imaging system, z is the imaging distance of the photon integrated interferometric imaging system, are the coordinates of the frequency sampling points of the photon integrated interferometric imaging system, and there are n groups of frequency sampling points in total.

[0081] S2: Calculate the reconstructed image The size of the image will be reconstructed Pad zero N times to obtain the frequency sampling points of the zero-padding image spectrum.

[0082] Reconstructing the image The calculation formula for the size is:

[0083] (2);

[0084] (3);

[0085] (4);

[0086] (5);

[0087] Among them, m is the size of the super-resolution reconstructed image, R is the number rounded up, is the ratio of the maximum frequency to the fundamental frequency of the photon integrated interferometric imaging system, is the maximum frequency of the photon integrated interferometric imaging system, is the fundamental frequency of the photon integrated interferometric imaging system, N is the zero-filling ratio, B min is the shortest paired baseline, B max is the longest paired baseline, is the minimum imaging wavelength of the photon integrated interferometric imaging system, is the maximum imaging wavelength of the photon integrated interferometric imaging system, and z is the imaging distance of the photon integrated interferometric imaging system.

[0088] S3: Generate a zero-padded spectrum mask using the frequency sampling points of the zero-padded image spectrum, and initialize the zero-padded image spectrum S using the zero-padded spectrum mask.

[0089] The calculation formula of zero-filled spectrum mask is:

[0090] (6);

[0091] (7);

[0092] (8);

[0093] in, is the coordinate of the nth group of frequency sampling points, N is the frequency sampling points expanded N times, P is the zero-filled spectrum mask, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

[0094] The formula for initializing the zero-padded image spectrum using the zero-padded spectrum mask is:

[0095] (9);

[0096] in, is the initialized zero-filled image spectrum, is the complex visibility of the nth group of frequency sampling points, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

[0097] S4: Inverse Fourier transform of the initialized zero-padded image spectrum into the spatial domain to obtain the initialized zero-padded image .

[0098] The formula for inverse Fourier transform of the initialized zero-filled image spectrum to the spatial domain is:

[0099] (10);

[0100] Among them, F -1 is the inverse Fourier transform, Initialize the zero-filled image The coordinates of is the initialized zero-padded image spectrum.

[0101] S5: construct a zero-filled image mask, and replace the zero-filled image mask with the reconstructed image The value of the area corresponding to the distribution area of ​​​​the reconstructed image is set to 1, and the zero-filled image mask that does not correspond to the reconstructed image The value of the area corresponding to the distribution area is set to 0.

[0102] In step S5, the formula of the zero-filled image mask is:

[0103] (11);

[0104] Where M is the value of the zero-filled image mask, Initialize the zero-filled image , m is the size of the super-resolution reconstructed image, and N is the zero padding factor.

[0105] S6: construct a spatial domain zero-padded image, and introduce the spatial domain zero-padded image gradient into the reconstruction objective function to obtain the reconstruction objective function after zero-padded.

[0106] S61: construct a spatial domain zero-filled image, and establish a reconstruction objective function based on the spatial domain zero-filled image and the reconstructed image:

[0107] (12);

[0108] (13);

[0109] (14);

[0110] in, is the zero-filling operation, P is the zero-filling spectrum mask, Ψ is the spectrum of the spatial zero-filled image, To initialize the zero-filled image spectrum, is the Fourier transform, x is the spatial domain zero-filled image, To reconstruct the image, is the fidelity term of the objective function;

[0111] S62: Introduce the spatial domain zero-filled image gradient into the reconstruction objective function through the following formula to obtain the reconstruction objective function after zero-filling:

[0112] (15);

[0113] Where P is the zero-filled spectrum mask, Ψ is the spectrum of the spatial domain zero-padded image, S is the spectrum of the initialized zero-padded image, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the inverse Fourier transform, is the Fourier transform, To reconstruct the image, For zero padding operation, w is the spatial domain zero-filled image gradient, is the penalty coefficient, || w ||1 represents anisotropic or isotropic TV regularization terms, and x is a zero-padded image in the spatial domain.

[0114] S7: The reconstructed objective function after zero padding is converted to the spatial domain for solution by the following formula:

[0115] (16);

[0116] (17);

[0117] (18);

[0118] (19);

[0119] in, Ψ is the spectrum of the spatial zero-filled image,w is the spatial domain zero-filled image gradient, is the penalty coefficient, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the anisotropic or isotropic TV regularization term, is the inverse Fourier transform, To initialize the zero-padded image, Zero-fill image in the spatial domain;

[0120] S8: Convert equations (16) to (19) into augmented Lagrangian multiplier function formulas, and use the alternating multiplier method to solve the augmented Lagrangian multiplier function to obtain the reconstructed zero-filled image.

[0121] Augmented Lagrange multiplier function The function expression is:

[0122] (20);

[0123] in, and is the Lagrange multiplier term, w is the spatial domain zero-filled image gradient, is the spatial zero-filled image, Ψ is the spectrum of the spatial zero-filled image, , and is the penalty coefficient, To initialize the zero-padded image, is the Fourier transform, is the inverse Fourier transform, ={D h , D v} is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, and P is the zero-filled spectrum mask.

[0124] S81: Assume Ψ, w , , The initial value of is 0, and the spatial domain is filled with zero images , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w The number of image rows and columns are both e and f, and the image is filled with zeros in the space domain. , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w As sub-problems of augmented Lagrange multiplier functions, the expressions of the three sub-problems are as follows:

[0125] (twenty one);

[0126] (twenty two);

[0127] (twenty three);

[0128] Where k is the number of iterations;

[0129] S82: Iteratively solve equations (21) to (23), and use the augmented Lagrange multiplier function to solve ,Ψ, w Take the derivative and get the updated , , The solution value of ;

[0130] S83: Repeat steps S81-S82 until k=100 or ( x k+1 - x k ) 2 / m / m<0.001, and the reconstructed zero-filled image is obtained.

[0131] S9: Use the zero-filled image mask to reconstruct the corresponding reconstructed image in the zero-filled image The target area is taken out to obtain a super-resolution reconstructed image.

[0132] like Figure 4-Figure 6 As shown, by comparing the reconstructed image obtained by processing the simulated high-resolution image using the traditional photon integrated interference imaging technology and the reconstructed image obtained by processing the simulated high-resolution image using the super-resolution image reconstruction method of photon integrated interference imaging, it can be seen that the super-resolution image reconstruction method of photon integrated interference imaging provided by the embodiment of the present invention has a better reconstruction effect than the traditional photon integrated interference imaging technology. The present invention can achieve the best reconstruction results for a variety of scenes, and can effectively cope with the actual application environment of photon integrated interference imaging. As shown in Table 1, the four groups of targets Lena, Resolution chart, Satellite, and Cameraman are the true values ​​of the simulation, and the mean square error (MSE) and signal-to-noise ratio (SNR) of the reconstructed images obtained by this method and the traditional method are on the left and right of the oblique line, respectively. As shown in Table 1, the mean square error and signal-to-noise ratio of the reconstructed image obtained by the present invention are much higher than those of the traditional method, and the reconstructed images for different scenes have strong robustness and are more suitable for practical applications.

[0133] Table 1

[0134]

[0135] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0136] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A super-resolution image reconstruction method for photon integrated interference imaging, characterized in that: The specific steps include: S1: Calculate the frequency sampling points of the photon integrated interferometric imaging system under non-uniform sparse sampling according to the baseline configuration and baseline pairing method of the photon integrated interferometric imaging system; S2: Calculate the reconstructed image size, and the reconstructed image Fill zero N times to obtain the frequency sampling points of the zero-filled image spectrum; S3: Generate a zero-padding spectrum mask using the frequency sampling points of the zero-padding image spectrum, and initialize the zero-padding image spectrum S using the zero-padding spectrum mask; S4: Inverse Fourier transform of the initialized zero-padded image spectrum into the spatial domain to obtain the initialized zero-padded image ; S5: construct a zero-filled image mask, and replace the zero-filled image mask with the reconstructed image The value of the area corresponding to the distribution area of ​​​​the reconstructed image is set to 1, and the zero-filled image mask that does not correspond to the reconstructed image The value of the area corresponding to the distribution area is set to 0; S6: construct a spatial domain zero-padded image, and introduce the spatial domain zero-padded image gradient into the reconstruction objective function to obtain the reconstruction objective function after zero-padded; S7: The reconstructed objective function after zero padding is converted to the spatial domain for solution by the following formula: （1）； （2）； （3）； （4）； in, Ψ is the spectrum of the spatial zero-filled image, w is the spatial domain zero-filled image gradient, is the penalty coefficient, ={D h , D v } is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the anisotropic or isotropic TV regularization term, is the inverse Fourier transform, To initialize the zero-padded image, Zero-fill image in the spatial domain; S8: converting equations (1) to (4) into an augmented Lagrangian multiplier function formula, and solving the augmented Lagrangian multiplier function using an alternating multiplier method to obtain a reconstructed zero-filled image; S9: Using the zero-padding image mask to reconstruct the corresponding reconstructed image in the reconstructed zero-padding image The target area is taken out to obtain a super-resolution reconstructed image.

2. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: In step S1, the calculation formula of the frequency sampling points of the photon integrated interference imaging system under non-uniform sparse sampling is: （5）； in,( , ) is the spatial coordinate of the p-th pairing baseline, is the jth imaging wavelength of the photon integrated interference imaging system, z is the imaging distance of the photon integrated interference imaging system, are the frequency sampling point coordinates of the photon integrated interference imaging system, and there are n groups of frequency sampling points in total.

3. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: In step S2, the image is reconstructed The size is calculated as: （6）； （7）； （8）； （9）； Among them, m is the size of the super-resolution reconstructed image, R is the number rounded up, is the ratio of the maximum frequency to the fundamental frequency of the photon integrated interferometric imaging system, is the maximum frequency of the photon integrated interferometric imaging system, is the fundamental frequency of the photon integrated interference imaging system, N is the zero filling ratio, B min is the shortest paired baseline, B max is the longest paired baseline, is the minimum imaging wavelength of the photon integrated interferometric imaging system, is the maximum imaging wavelength of the photon integrated interference imaging system, and z is the imaging distance of the photon integrated interference imaging system.

4. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: In step S3, the calculation formula of the zero-filled spectrum mask is: （10）； （11）； （12）； in, is the coordinate of the nth group of frequency sampling points, N is the N-fold expansion of the frequency sampling points, P is the zero-filled spectrum mask, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

5. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 4 is characterized in that: In step S3, the formula for initializing the zero-padded image spectrum using the zero-padded spectrum mask is: （13）； in, is the initialized zero-filled image spectrum, is the complex visibility of the nth group of frequency sampling points, To expand the horizontal coordinate of the nth group of frequency sampling points by N times, The vertical coordinate of the nth group of frequency sampling points expanded N times.

6. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: In step S4, the formula for inverse Fourier transform of the initialized zero-filled image spectrum to the spatial domain is: （14）； Among them, F -1 is the inverse Fourier transform, Initialize the zero-filled image The coordinates of is the initialized zero-filled image spectrum.

7. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: In step S5, the formula of the zero-filled image mask is: （15）； Where M is the value of the zero-filled image mask, Initialize the zero-filled image , m is the size of the super-resolution reconstructed image, and N is the zero padding factor.

8. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 1, characterized in that: Step S6 specifically includes the following steps: S61: construct a spatial domain zero-filled image, and establish a reconstruction objective function based on the spatial domain zero-filled image and the reconstructed image: （16）； （17）； （18）； in, is the zero-filling operation, P is the zero-filling spectrum mask, Ψ is the spectrum of the spatial zero-filled image, To initialize the zero-filled image spectrum, is the Fourier transform, x is the spatial domain zero-filled image, To reconstruct the image, is the fidelity term of the objective function; S62: introducing the spatial domain zero-filled image gradient into the reconstruction objective function by the following formula to obtain the reconstruction objective function after zero-filling: （19）； Where P is the zero-filled spectrum mask, Ψ is the spectrum of the spatial domain zero-padded image, S is the spectrum of the initialized zero-padded image, ={D h , D v } is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, is the inverse Fourier transform, is the Fourier transform, To reconstruct the image, For zero padding operation, w is the spatial domain zero-filled image gradient, is the penalty coefficient, || w ||1 represents anisotropic or isotropic TV regularization terms, and x is a zero-padded image in the spatial domain.

9. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 8, characterized in that: In step S8, the augmented Lagrange multiplier function The function expression is: （20）； in, and is the Lagrange multiplier term, w is the spatial domain zero-filled image gradient, is the spatial zero-filled image, Ψ is the spectrum of the spatial zero-filled image, , and is the penalty coefficient, To initialize the zero-padded image, is the Fourier transform, is the inverse Fourier transform, ={D h , D v } is the gradient operator, D h is the transverse gradient operator, D v is the longitudinal gradient operator, and P is the zero-filled spectrum mask.

10. The super-resolution image reconstruction method of photon integrated interference imaging according to claim 9, characterized in that: Step S8 specifically includes the following steps: S81: Assume Ψ, w , , The initial value of is 0, and the spatial domain is filled with zero images , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w The number of image rows and columns are both e and f, and the image is filled with zeros in the space domain. , the spectrum Ψ of the spatial zero-filled image and the gradient of the spatial zero-filled image w As sub-problems of the augmented Lagrange multiplier function, the expressions of the three sub-problems are as follows: （21）； （22）； （23）； Where k is the number of iterations; S82: Iteratively solve equations (21) to (23), and use the augmented Lagrange multiplier function to solve ,Ψ, w Take the derivative and get the updated , , The solution value of ; S83: Repeat steps S81-S82 until k=100 or ( x k+1 - x k ) 2 / m / m<0.001, and the reconstructed zero-filled image is obtained.

Images