Sparse Image Reconstruction Method Based on Non-Uniform Fourier Transform

Abstract

The present invention relates to the field of photon integrated interference imaging technology, and in particular to a sparse image reconstruction method based on non-uniform Fourier transform. It includes: S1: calculating the frequency sampling point coordinates of the photon integrated interference imaging system according to the baseline configuration and baseline pairing method of the photon integrated interference imaging system: S2: calculating the size of the reconstructed image; S3: constructing a non-uniform Fourier transform matrix for calculating the reconstructed image; S4: calculating the reconstructed image according to the non-uniform Fourier transform matrix; S5: rearranging the reconstructed image from a one-dimensional column matrix to a two-dimensional column matrix according to the size of the reconstructed image to obtain the final reconstructed image. The present invention can accurately describe the sampling frequency of the photon integrated interference imaging system and effectively improve the quality of image reconstruction.

Description

Technical Field

[0001] The invention relates to the technical field of photon integrated interference imaging, and in particular to a sparse image reconstruction method based on non-uniform Fourier transform. Background Art

[0002] In the field of astronomical observation and remote sensing imaging, in order to improve the imaging resolution of the optical system, it is usually chosen to increase the aperture of the optical system. However, as the aperture of the optical system increases, its manufacturing cost increases exponentially. The photon integrated interferometric imaging system provides a new technical approach to replace the traditional large-aperture optical system. The use of photon integrated chip (PIC) to realize the beam synthesis of the interference array can significantly improve the system's real-time, sensitivity, and scalability, and effectively enhance the system's stability and reliability. The processing and manufacturing are simple, the process is stable, and the manufacturing cost is effectively reduced. However, unlike the imaging mode in the traditional Cartesian coordinate system, the frequency sampling method in the photon integrated interferometric imaging system is polar coordinate sampling, which results in the sampling method of the photon integrated interferometric imaging system being discrete sampling, and the sampling frequency is non-integer sampling, while the traditional discrete Fourier transform method is prone to cause a large number of frequency missing, and the discrete Fourier transform method has great limitations. Summary of the invention

[0003] In order to solve the problems that the frequency sampling method in the photon integrated interferometric imaging system is polar coordinate sampling, the traditional discrete Fourier transform method is prone to cause a large number of frequency missing and the discrete Fourier transform method has great limitations, a sparse image reconstruction method based on non-uniform Fourier transform is provided, which can effectively deal with the problems caused by sparse sampling and non-uniform sampling under polar coordinates.

[0004] The sparse image reconstruction method based on non-uniform Fourier transform provided by the present invention is implemented by using a photon integrated interference imaging system, and 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 point coordinates of the photon integrated interferometric imaging system are calculated by the following formula:

[0006] (1);

[0007] Among them, B p is the paired baseline of group p, is the jth imaging wavelength of the photon integrated interferometric imaging system, z is the imaging distance of the photon integrated interferometric imaging system, is the frequency sampling point of the photon integrated interferometric imaging system, and there are n groups of frequency sampling points in total, ( x , y ) is the spatial coordinate;

[0008] S2: Combined with formula (1), the size m of the reconstructed image is calculated by the following formula:

[0009] (2);

[0010] (3);

[0011] (4);

[0012] (5);

[0013] Among them, 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, 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;

[0014] S3: According to the frequency sampling point coordinates of the photon integrated interferometric imaging system, a non-uniform Fourier transform matrix F is constructed for calculating the reconstructed image:

[0015] (6);

[0016] S4: According to the non-uniform Fourier transform matrix, the reconstructed image I is calculated by the following formula:

[0017] (7);

[0018] (8);

[0019] (9);

[0020] in, is the complex visibility distribution of the frequency sampling points of the imaging target of the photon integrated interferometric imaging system, is the complex visibility of the nth group of frequency sampling points, is the phase of the complex visibility of the nth frequency sampling point, is the modulus of the complex visibility of the nth group of frequency sampling points;

[0021] S5: rearrange the reconstructed image from the one-dimensional column matrix to the two-dimensional column matrix according to the size of the reconstructed image to obtain a final reconstructed image.

[0022] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0023] The sparse image reconstruction method based on non-uniform Fourier transform proposed in the present invention can accurately describe the sampling frequency of the photon integrated interference imaging system, avoid the problems of frequency redundancy and frequency approximation error under traditional discrete sampling, and effectively improve the quality of image reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flow chart of a sparse image reconstruction method based on non-uniform Fourier transform provided according to an embodiment of the present invention;

[0025] Figure 2 is a schematic diagram of a SPIDER subaperture array arrangement according to an embodiment of the present invention;

[0026] Figure 3 is a simulation image provided according to an embodiment of the present invention;

[0027] Figure 4 It is a reconstructed image obtained based on the discrete Fourier transform method;

[0028] Figure 5 It is a reconstructed image obtained by the sparse image reconstruction method based on non-uniform Fourier transform provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0030] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present 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 herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0031] Figure 1 The flowchart of the sparse image reconstruction method based on non-uniform Fourier transform provided according to an embodiment of the present invention is shown.

[0032] like Figure 1 As shown, the sparse image reconstruction method based on non-uniform Fourier transform provided by the present invention is implemented by using a photon integrated interference imaging system, and specifically includes the following steps:

[0033] S1: According to the baseline configuration and baseline pairing method of the photon integrated interferometric imaging system, the frequency sampling point coordinates of the photon integrated interferometric imaging system are calculated by the following formula:

[0034] (1);

[0035] Among them, B p is the paired baseline of group p, is the jth imaging wavelength of the photon integrated interferometric imaging system, z is the imaging distance of the photon integrated interferometric imaging system, is the frequency sampling point of the photon integrated interferometric imaging system, and there are n groups of frequency sampling points in total, ( x , y ) are spatial coordinates;

[0036] S2: Combined with formula (1), the size m of the reconstructed image is calculated by the following formula:

[0037] (2);

[0038] (3);

[0039] (4);

[0040] (5);

[0041] Among them, 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, 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;

[0042] S3: According to the frequency sampling point coordinates of the photon integrated interferometric imaging system, a non-uniform Fourier transform matrix F is constructed for calculating the reconstructed image:

[0043] (6);

[0044] S4: According to the non-uniform Fourier transform matrix, the reconstructed image I is calculated by the following formula:

[0045] (7);

[0046] (8);

[0047] (9);

[0048] in, is the complex visibility distribution of the frequency sampling points of the imaging target of the photon integrated interferometric imaging system, is the complex visibility of the nth group of frequency sampling points, is the phase of the complex visibility of the nth frequency sampling point, is the modulus of the complex visibility of the nth group of frequency sampling points;

[0049] S5: rearrange the reconstructed image from the one-dimensional column matrix to the two-dimensional column matrix according to the size of the reconstructed image to obtain a final reconstructed image.

[0050] Figure 2 A SPIDER sub-aperture array arrangement diagram provided according to an embodiment of the present invention is shown.

[0051] like Figure 2 As shown, a single interferometer arm has 60 sub-apertures, and the imaging band of the photon integrated interferometric imaging system is 1470nm-1670nm. The imaging band of 1470nm-1670nm is divided into five spectral segments, and the interval between adjacent spectral segments is 40nm, so the number of complex visibility V is 12960.

[0052] Figure 3 shows a simulation image provided according to an embodiment of the present invention, Figure 4 shows the reconstructed image obtained based on the discrete Fourier transform method, Figure 5 The reconstructed image obtained by the sparse image reconstruction method based on non-uniform Fourier transform provided by an embodiment of the present invention is shown.

[0053] like Figure 3-Figure 5 As shown, the sparse image reconstruction method based on discrete Fourier transform and the sparse image reconstruction method based on non-uniform Fourier transform provided by the embodiment of the present invention are respectively used to reconstruct the image as shown in FIG. Figure 3 The simulation image shown is reconstructed, and the corresponding Figure 4-Figure 5 The reconstructed image shown proves the feasibility of the sparse image reconstruction method based on non-uniform Fourier transform proposed in the present invention.

[0054] 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.

[0055] 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 sparse image reconstruction method based on non-uniform Fourier transform, implemented using a photon integrated interference imaging system, characterized in that: The specific steps include: S1: According to the baseline configuration and baseline pairing method of the photon integrated interferometric imaging system, the frequency sampling point coordinates of the photon integrated interferometric imaging system are calculated by the following formula: （1）； Among them, B p is the paired baseline of group p, is the jth imaging wavelength of the photon integrated interference imaging system, z is the imaging distance of the photon integrated interference imaging system, is the frequency sampling point coordinate of the photon integrated interference imaging system, and there are n groups of frequency sampling points in total, ( x , y ) is the spatial coordinate; S2: Combined with formula (1), the size m of the reconstructed image is calculated by the following formula: （2）； （3）； （4）； （5）； Among them, R is the number rounded up, is the ratio of the maximum frequency to the fundamental frequency of the photon integrated interference imaging system, is the maximum frequency of the photon integrated interferometric imaging system, is the fundamental frequency of the photon integrated interferometric imaging system, 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; S3: According to the frequency sampling point coordinates of the photon integrated interference imaging system, a non-uniform Fourier transform matrix F for calculating the reconstructed image is constructed: （6）； S4: According to the non-uniform Fourier transform matrix, the reconstructed image I is calculated by the following formula: （7）； （8）； （9）； in, is the complex visibility distribution of the frequency sampling points of the imaging target of the photon integrated interferometric imaging system, is the complex visibility of the nth group of frequency sampling points, is the phase of the complex visibility of the nth frequency sampling point, is the modulus of the complex visibility of the nth group of frequency sampling points; S5: rearrange the reconstructed image from a one-dimensional column matrix to a two-dimensional column matrix according to the size of the reconstructed image to obtain a final reconstructed image.

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