Incoherent super-resolution imaging method based on mixed state decomposition
By using a mixed-state decomposition filter and a frequency broadening weighting factor, the reconstruction quality problem of Fourier stacked imaging under low coherence conditions was solved, realizing the restoration of high-resolution images and the expansion of applications.
Patent Information
- Application Number
- CN202511391515.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-26
- Publication Date
- 2026-01-20
AI Technical Summary
Existing Fourier layer imaging techniques suffer from reduced image resolution and enhanced artifacts under conditions of spatial coherence degradation, and their application scenarios are limited, making them unsuitable for complex environments.
An incoherent super-resolution imaging method based on mixed-state decomposition is adopted. By constructing a mixed-state decomposition filter and introducing a frequency broadening weighting factor, the image coherence is enhanced, and a high-resolution image is reconstructed iteratively using an optimization function.
Under low spatial coherence conditions, it significantly improves image resolution and clarity, expands application scenarios, and is suitable for microscopic imaging, long-distance imaging, and complex scattering environments.
Smart Images
Figure CN121366080A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of synthetic aperture imaging, and particularly relates to a non-coherent super-resolution imaging method based on mixed state decomposition. BACKGROUND
[0002] Fourier ptychographic imaging is a non-interferometric synthetic aperture imaging technology. Its basic principle is to collect multiple offset spectrum information of a target in the frequency domain, and then use an iterative reconstruction algorithm to splice and fuse the spectrum, thereby breaking through the diffraction limit of a single physical aperture and achieving high-resolution imaging. Since this method does not rely on an interference optical path, the system structure is relatively simple, and in principle, it can obtain a resolution close to that of a large-aperture system under limited numerical aperture conditions, thus having broad application prospects in the fields of optical microscopic imaging, remote sensing detection, space imaging, etc.
[0003] However, the theoretical model of Fourier ptychographic imaging technology is based on a light field with high spatial coherence. Under laboratory conditions, a relatively ideal imaging effect can be achieved by using coherent laser or filtered high-coherence light sources. However, in actual application scenarios, the spatial coherence of the light field often degenerates due to the following reasons: Light source characteristics limit: Actual light sources are often partially coherent light, such as LEDs or light fields after scattering, which have limited spatial coherence length and are difficult to meet the strict coherence requirements.
[0004] Propagation medium disturbance: atmospheric turbulence, haze, smoke, and underwater environments all introduce random scattering effects, causing rapid decay of the spatial coherence of the light field.
[0005] Complex detection conditions: In long-distance imaging, the target size is large, and the light field collected by the imaging system usually contains the superposition of multiple modes, reducing the proportion of effective coherent components.
[0006] Under the condition of degradation of the spatial coherence of the light field, Fourier ptychographic imaging faces the following prominent problems: First, the super-resolution effect will decrease, and the resolution of the reconstructed image will be significantly lower than the theoretical expectation, making it difficult to distinguish the details of the target; second, the reconstructed image artifacts are enhanced: since the original data no longer meet the coherent imaging model, obvious artifacts and noise enhancement occur during the iterative reconstruction process; finally, the imaging applicability is limited, and Fourier ptychographic technology is difficult to apply to actual complex environments, such as aerospace remote sensing, military confrontation detection, etc.
[0007] Therefore, how to effectively extract and restore the coherent information in the original collected image under the condition of degradation of the spatial coherence, so that it can still meet the reconstruction requirements of Fourier ptychographic imaging, is a core problem that needs to be solved in this field.
[0008] The existing Fourier ptychographic imaging method mainly relies on aperture scanning, camera scanning, spherical wave illumination, camera array acquisition and other schemes in the implementation path. Although many researchers have made certain explorations on the long-distance ptychographic imaging under the macroscopic imaging conditions based on the Fourier ptychographic in the microscopic field and the coherent imaging field, the long-distance super-resolution imaging potential is achieved. These researches have made certain progress in expanding the system configuration, improving the resolution and the field of view. However, the further application of the technology in the long-distance scene is restricted based on the coherent imaging model, and the following defects exist: 1. Dependence on high spatial coherence conditions: Most of the above methods are based on the assumption of ideal or approximately ideal spatial coherence light field. When the coherence of the light field is degraded, the original image collected no longer satisfies the reconstruction model of the Fourier ptychographic imaging, so that the super-resolution capability is difficult to achieve.
[0009] 2. Unstable reconstruction quality: In a low-coherence or complex scattering environment, the reconstructed image often has problems such as resolution decline, artifact enhancement and detail loss, which seriously affects the actual application value.
[0010] 3. Limited application scenarios: Due to the strict requirement of coherence, the existing technology is difficult to be applied to remote sensing monitoring in a long-distance imaging and atmospheric disturbance environment, military confrontation detection and biological tissue imaging in actual complex environments. SUMMARY
[0011] In order to solve the above problems in the prior art, the present application provides a non-coherent super-resolution imaging method based on mixed state decomposition. The technical problems to be solved by the present application are solved by the following technical solutions: A non-coherent super-resolution imaging method based on mixed state decomposition comprises: S100, based on the Fourier ptychographic system forward imaging principle under spatial coherence degradation, a plurality of low-resolution images of any object are collected; S200, a mixed state decomposition filter is constructed according to the plurality of low-resolution images; S300, the mixed state filter is used to filter the plurality of low-resolution images to obtain a coherence-enhanced image; S400, for any low-resolution image, the intensity of the high-resolution image to be reconstructed for the low-resolution image is initially guessed to obtain a high-resolution spectrum; wherein the high-resolution spectrum is composed of the low-resolution spectra of all low-resolution images; S500, for each low-resolution image, an optimization function is set to minimize the difference between the intensity of the high-resolution image and the intensity of the low-resolution image by using the low-resolution image, the high-resolution spectrum, the coherence-enhanced image and the corresponding transfer function; S600, optimizing the optimization function through a loop iteration to obtain a high-resolution image.
[0012] Advantages: 1. The prior art usually assumes that the illumination light source is completely coherent or quasi-coherent, and it is difficult to accurately depict the spatial coherence degradation effect in the actual imaging process. The present application compensates for the spectral broadening and frequency leakage caused by spatial incoherence by introducing a frequency broadening weight factor in the Fourier superposition imaging forward model, so that the light field propagation and image formation process under low coherence conditions can be more truly reflected, and the consistency of the model and experimental observation is improved.
[0013] 2. The prior art does not effectively compensate for the aliasing and loss of image frequency information caused by spatial incoherence degradation, resulting in limited reconstruction resolution and poor quality of reconstructed images. The mixed state decomposition filter proposed in the present application enhances the independent distinguishability of target frequency response and specific frequency through matrix operation without the need for additional measurement of light field coherence, further improves the high-frequency recovery ability under low spatial coherence conditions, and thus significantly improves the resolution and clarity of the final reconstructed image.
[0014] 3. The existing method relies on specific light source conditions or strict system stability requirements, and has insufficient migration and universality; the filter and modeling method proposed in the present application does not depend on specific light source form, can be widely applied to various light source conditions, and can be adjusted according to different spatial coherence degradation levels without the need for additional measurement of light field coherence, thus having strong migration ability and being applicable to microscopic imaging, long-distance imaging, and complex scattering environment imaging and other scenes affected by spatial coherence degradation.
[0015] The present application will be further described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS
[0016] Figure 1 is a flowchart of a non-coherent super-resolution imaging method based on mixed state decomposition provided by the present application; Figure 2 is a Fourier superposition system forward imaging system; Figure 3 is a Fourier superposition coherence degradation collected original low-resolution image; Figure 4 is a coherence enhanced image provided by the present application; Figure 5 is a comparison chart of the traditional method and the mixed state decomposition method of the present application. DETAILED DESCRIPTION
[0017] The application will be described in further detail below with reference to specific embodiments, but the embodiments of the application are not limited thereto.
[0018] In view of the dependence of the traditional macroscopic Fourier superposition imaging method on the coherent imaging model, the application provides a macroscopic Fourier superposition non-coherent imaging method based on mixed state decomposition. The method constructs a differential directional filter in the reconstruction process, which weakens the common mode (low frequency) component and enhances the directional sensitive high frequency, and partially compensates for the spectral broadening and frequency leakage caused by spatial non-coherence. That is, under the condition of spatial non-coherence, this filter enhances the frequency structure that is erased due to the frequency broadening caused by the degradation of coherence through directional differentiation.
[0019] According to the Van Cittert-Zernike theorem, the angular divergence of the spatial non-coherent light source will cause the width of the coherence function on the observation surface to narrow, that is, each point in the image becomes an average of multiple directional illumination results, which destroys the frequency selective coding required for Fourier superposition imaging. In order to compensate for this frequency aliasing phenomenon, the coherence enhancement method based on directional selective differentiation proposed by the application enhances the target frequency response from mixed angle illumination without increasing the amount of collected data by using the difference in frequency response between different data in the original data array to construct a directional filter operator. This is equivalent to establishing an inverse selective frequency enhancement mechanism under the Van Cittert-Zernike effect in the spatial domain, thereby performing deconvolution operation on the frequency broadening under the coherence degradation, enhancing the independent distinguishability of specific frequencies, and further improving the edge frequency recovery capability under the condition of low spatial coherence.
[0020] As shown in Figure 1 , the application provides a non-coherent super-resolution imaging method based on mixed state decomposition, which comprises: S100, based on the Fourier superposition system forward imaging principle under spatial coherence degradation, collecting multiple low-resolution images of any object; In a specific embodiment of the application, S100 comprises: S110, using the light field definition and the angle autocorrelation function in the Fourier superposition system forward imaging principle under spatial coherence degradation, collecting the light field filtered by the optical system low pass filter when the camera scans to different positions in the far field , thereby generating multiple original low-resolution images; Reference Figure 2 , Figure 2 is a Fourier superposition system forward imaging system, and the system camera scans the target, that is, any object, at different positions, and the light source is irradiated on the target through an illumination lens and a rotating diffuser.
[0021] In a specific embodiment of the application, S110 comprises: S111, determine the light field based on the imaging principle of the camera; Marchand and Wolf proposed to use angular spectrum expansion to study the far-field statistical properties of partially coherent fields. In frequency The light field can be represented as a superposition of plane waves propagating in different directions, i.e., the light field is expressed as: (1) where, is the propagation direction, , is the angular spectrum complex amplitude function, which describes the complex amplitude of the plane wave propagating in direction at frequency , is the distance from the point to the light source; S112, introduce an angular autocorrelation function in the light field to obtain the total light intensity in any propagation direction; To describe the statistical correlation between different angles, an angular autocorrelation function is introduced, which is expressed as: (2); where, and represent two propagation directions, when , , represents or the intensity of the plane wave in the direction, the superscript * represents the complex conjugate.
[0022] This function defines the statistical correlation of the complex amplitudes of the plane waves in two propagation directions and at frequency . It not only contains amplitude information, but also reflects the degree of coherence. In particular, when , , represents the intensity of the plane wave in the direction. Marchand and Wolf further proved that the angular correlation function has a Fourier transform relationship with the cross-spectral density function on the source plane. That is, the correlation of different directions in the angular spectrum is derived from the spatial correlation between different points on the light source plane, which is projected into the direction space through Fourier transform. This method can fully characterize the coherence properties in the angular structure and realize the statistical mapping from the spatial domain to the direction domain. Further, starting from the angular spectrum expansion, Marchand and Wolf derived the expression of the total light intensity in a certain direction in the far field: (3); where, represents the inclination angle of the point relative to the optical axis; S113, Based on the total light intensity, determine the superposition of incoherent frequencies of light intensity at any angle as an autocorrelation function; Equation (2) indicates that the light intensity in a fixed direction in the far field is the integral of the angular autocorrelation function corresponding to that direction in the frequency dimension, i.e., the superposition of incoherent frequencies under a fixed angular direction. This is a generalization of the traditional van Sitzernik conclusion, allowing for consideration of practical scenarios where there is finite coherence between angular directions. When fully coherent light illuminates, the distribution of the angular autocorrelation function is close to the Dirac function, indicating that energy is concentrated in a specific direction, i.e., light propagates along a specific direction. However, when partially spatially coherent light illuminates, the angular autocorrelation function has finite broadening, i.e., non-zero energy is not limited to a single direction, but spreads within an angular range. This property shows that, from a geometric optics perspective, light passing through a spatial point no longer propagates in one direction, but instead propagates in multiple directions, forming a fan-shaped energy flux density with finite angular broadening. This fan-shaped structure reflects the directional divergence phenomenon caused by partial coherence and is also a simplified description of angular spectrum broadening under partial coherence conditions.
[0023] S114, based on the principle of superposition of incoherent frequencies where light intensity at any angle is an autocorrelation function, acquires multiple raw low-resolution images from the camera.
[0024] In camera-scanning Fourier layered imaging, the camera scans to different positions in the far field. At that time, a low-resolution image is generated by acquiring the light field after it has been low-pass filtered by the optical system. It can be represented as: (4); In the formula, Indicates the sampling location The original low-resolution image acquired below. In spatial location Spatial frequency coordinates at that location For high-resolution spectrum, For the intensity of high-resolution images, For Fourier transform, To be at the sampling location The spatial frequency coordinates below To be at the sampling location The transfer function of the camera's optical system is expressed as: (5); In the formula, For the maximum spatial frequency, For wave number, For illumination wavelength, The numerical aperture of the optical system. It represents the spatial radial frequency.
[0025] S120, based on the angle autocorrelation function in any direction, the contribution of total light intensity, and introducing a frequency spread weight factor, the original low-resolution image is corrected to obtain a plurality of low-resolution images.
[0026] Under coherent conditions, considering the interaction of transfer function and target spectrum, the collected image has obvious frequency selection characteristics. When the spatial coherence is degraded, the originally specific frequency of the illumination light is spread, forming a mixed illumination component of multiple incident angles. At this time, although the camera only collects the signal of one aperture position, each position image is affected by the illumination result of multiple angle components. Figure 3 As shown, Figure 3 The original low-resolution image collected by Fourier superposition under the condition of coherence degradation. In Figure 3 Fig. (a) is an image collected under laser illumination, Fig. (b) is an image collected under LED illumination, and Fig. (c) is an image collected under LED single-layer tissue paper illumination. According to the contribution of the reference angle autocorrelation function (2) in formula (3), the low-resolution image is represented by formula: (6); In the formula, The weight factor of frequency spread is represented by The shift amount of the transfer function in the x and y directions is represented by The shift amount of the transfer function in the x and y directions is represented by And The shift amount of the transfer function in the x and y directions is represented by
[0027] At this time, the low-resolution image can be regarded as the incoherent superposition of the target spectrum intercepted by multiple shifted transfer functions. The image formed by each aperture position is the intensity superposition result of the images under multiple angles.
[0028] The present application introduces a frequency spread weight factor on the basis of the traditional Fourier superposition imaging model, and corrects the imaging process under the condition of insufficient spatial coherence of light field, breaks through the limitation of the traditional Fourier superposition imaging model which highly depends on the coherent imaging condition, and provides theoretical support for high-quality reconstruction under low-coherence condition.
[0029] S200, constructing a mixed state decomposition filter according to the plurality of low-resolution images; In a specific embodiment of the present application, S200 includes: S210, unfolding each low-resolution image into a column vector, and stacking all column vectors into an image position matrix according to the position index of the low-resolution image; The camera scans at positions, and obtains low-resolution images , wherein , . The is expanded as a column vector: , and the amplitude image is stacked as an image position matrix matrix according to the position index: (7); wherein, , , , represents a low-resolution image; S220, for any low-resolution image index in the image position matrix, determine the index of the two symmetric images of the low-resolution image in the image position matrix; Any low-resolution image index in the image position matrix is represented as: (8); The index of the two symmetric images in the image position matrix is represented as (9); wherein, represents the index of the symmetric image in the image position matrix, represents the index of the symmetric image in the image position matrix; S230, determine the center region coordinates of the image position matrix, and determine the center region using the center region coordinates; The center region coordinates of the image position matrix are defined as: (10); The center region is represented as: (11); S240, construct a mixed state decomposition filter using the center region. In order to suppress the frequency leakage caused by the degradation of spatial coherence, the mixed state decomposition filter is constructed
[0030] , and the mixed state decomposition filter is represented as: (12); wherein, , respectively represent the elements in the matrix , and the two subscripts correspond to the row and column of the element, , , is an empirical constant between 0 and 1, is the number of images in the central region.
[0031] , , is an empirical constant between 0 and 1, is the number of images in the central region.
[0032] The present application designs a mixed-state decomposition filter, under the premise of not increasing the amount of collected data, performs coherence mixed-state decomposition on the collected low-resolution images, performs deconvolution operation on the frequency spread under coherence degradation, thereby effectively suppressing the incoherent components in the original image while enhancing the target coherent components; the filter can be formalized as a matrix operation on an image array, and the weight can be adaptively adjusted according to the degree of spatial coherence degradation.
[0033] S300, filtering a plurality of low-resolution images by using the mixed-state filter to obtain a coherence-enhanced image; then the coherence-enhanced image obtained after the filter acts is: (13); In the formula, represents a matrix composed of all low-resolution images, represents a mixed-state decomposition filter, represents a coherence-enhanced image. Referring to Figure 4 , it can be seen that Figure 4 is a coherence-enhanced image. Figure 4 In FIG., (a) is an image before enhancement, and (b) is a coherence-enhanced image.
[0034] S400, for any low-resolution image, performing initial guess on the intensity of a high-resolution image which needs to be reconstructed from the low-resolution image to obtain a high-resolution frequency spectrum; wherein the high-resolution frequency spectrum is composed of low-resolution frequency spectra of all low-resolution images; The high-resolution frequency spectrum is expressed by a formula as: (14); In the formula, represents a spatial domain coordinate.
[0035] S500, for each low-resolution image, using the low-resolution image, the high-resolution frequency spectrum, the coherence-enhanced image, and the corresponding transfer function to set an optimization function which minimizes the difference between the intensity of the high-resolution image and the intensity of the low-resolution image; The optimization function in S500 is expressed by a formula as: (15); wherein, represents a low resolution image collected at a sampling position .
[0036] S600, optimizing the optimization function through loop iteration to obtain a high resolution image.
[0037] In a specific embodiment of the present application, S600 comprises: S610, for each low resolution image, calculating a low resolution light field corresponding to the low resolution image by using the high resolution spectrum and the transfer function corresponding to the low resolution image. The high resolution target is low-pass filtered by the optical system and scanned to different positions recorded by the camera as intensity information, at this time, the low resolution light field recorded by the camera is: (16); wherein, represents a low resolution light field; S620, extracting an enhanced image corresponding to each low resolution image from the coherence-enhanced image; S630, for each low resolution image, replacing the low resolution light field corresponding to the low resolution image with the enhanced image to obtain a replaced light field; The replaced light field is represented by the formula: (17); wherein, represents a replaced light field, represents an enhanced image; S640, for each low resolution image, transforming the replaced light field to the frequency domain to obtain a light field in the frequency domain; S650, for each low resolution image, updating the low resolution spectrum corresponding to the low resolution image in the high resolution spectrum by using the light field in the frequency domain to obtain an updated high resolution spectrum; the updated high resolution spectrum is represented by the formula: (18); wherein, is a step size parameter for updating, represents a complex conjugate operation.
[0038] S660, repeating S610 to S650 to obtain the updated high resolution spectrum when the optimization function is minimized; Repeat S610 to S650 until the reconstruction algorithm reaches a convergent state, so as to consider that the reconstruction process of the high resolution target spectrum is completed, and inverse Fourier transform is performed to obtain a high resolution intensity image of the target The goal of the iterations of the reconstruction algorithm is to minimize the difference between the estimated light field corresponding intensity information and the actually acquired low resolution intensity information.
[0039] S670, performing Fourier transform on the updated high resolution spectrum at the minimum of the optimization function to obtain a high resolution image.
[0040] Reference Figure 5 , Figure 5 The contrast image of the traditional method and the mixed state decomposition method of the present application, Figure 5 In the figure (a) is the original low resolution, (b) is the image reconstructed by the traditional method, (c) is the image reconstructed by the mixed state decomposition method of the present application. Obviously, the quality of the image reconstructed by the present application is higher than that of the traditional method.
[0041] The method proposed in the present application does not depend on specific light source or imaging system parameters, and does not need to make additional coherence measurement on the light field; in addition to macro Fourier superposition imaging, it can be applied to other coherent-incoherent coupled light field imaging systems and imaging scenes limited by spatial coherence, and has good migration and universality.
[0042] The above is a further detailed description of the present application in combination with specific preferred embodiments, and cannot be considered as limiting the specific implementation of the present application to these descriptions. For ordinary skilled persons in the technical field to which the present application belongs, a number of simple deductions or substitutions can be made without departing from the concept of the present application, and all of them should be considered as falling within the protection scope of the present application.
Claims
1. A non-coherent super-resolution imaging method based on mixed-state decomposition, characterized in that, Comprising: S100, based on the Fourier superposition system forward imaging principle under spatial coherence degradation, collecting multiple low-resolution images of any object; S200, constructing a mixed state decomposition filter according to the multiple low-resolution images; S300, filtering the multiple low-resolution images by using the mixed state filter to obtain coherence enhanced images; S400, for any low-resolution image, performing initial guess on the intensity of the high-resolution image to be reconstructed for the low-resolution image to obtain a high-resolution spectrum; wherein the high-resolution spectrum is composed of low-resolution spectra of all low-resolution images; S500, for each low-resolution image, using the low-resolution image, the high-resolution spectrum, the coherence enhanced image and the corresponding transfer function to set an optimization function that minimizes the difference between the intensity of the high-resolution image and the intensity of the low-resolution image; S600, optimizing the optimization function through cyclic iteration to obtain a high-resolution image.
2. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 1, characterized in that, S100 comprises: In S110, the light field definition in the forward imaging principle of the Fourier superposition system under spatial coherence degradation and the angle autocorrelation function are used to collect the light field of the camera in the far field scanning to different positions low-pass filtered by the optical system, thereby generating a plurality of original low-resolution images; S120, based on the contribution of the total light intensity in any direction of the angular autocorrelation function, and introducing a frequency spread weight factor to correct the original low-resolution image to obtain multiple low-resolution images.
3. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 2, characterized in that, S110 comprises: S111, determining the light field based on the imaging principle of the camera; S112, introducing an angular autocorrelation function in the light field to obtain the total light intensity in any propagation direction; S113, based on the total light intensity, determining that any angle light intensity is a non-coherent frequency superposition of the autocorrelation function; S114, based on the principle that any angle light intensity is a non-coherent frequency superposition of the autocorrelation function, collecting multiple original low-resolution images from the camera.
4. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 3, characterized in that, The light field in S111 is expressed by the formula: （1） wherein is the direction of propagation, , is the angular spectrum complex amplitude function, describing the complex amplitude of a plane wave propagating in direction at frequency , is the distance of the point from the light source; The angular autocorrelation function in S112 is expressed by the formula: （2）； where and denote two propagation directions, when , , denote or the intensity of a plane wave in the direction, the superscript * denotes the complex conjugate; The total light intensity in S112 is expressed by the formula: （3）； In the formula, denotes the angle of inclination of the point relative to the optical axis; The original low-resolution image in S114 is expressed by the formula: （4）； wherein denotes the original low-resolution image acquired at sampling positions , is the spatial frequency coordinate at spatial position , is the high-resolution spectrum of any object , is the Fourier transform, is the spatial frequency coordinate at sampling positions , is the transfer function of the optical system of the camera at sampling positions , denoted by （5）； wherein is the maximum spatial frequency, is the wave number, is the illumination wavelength, is the numerical aperture of the optical system, is the spatial radial frequency.
5. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 4, characterized in that, The low-resolution image in S120 is expressed by the formula: （6）； wherein denotes a weight factor for the frequency spread, denotes and denote the offset of the transfer function in the and directions, respectively.
6. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 5, characterized in that, S200 comprises: S210, expanding each low-resolution image into a column vector, and stacking all column vectors into an image position matrix according to the position index of the low-resolution image; S220, for the index of any low-resolution image in the image position matrix, determining the index of the two symmetric images of the low-resolution image in the image position matrix; S230, determining the center region coordinates of the image position matrix, and determining the center region by using the center region coordinates; S240, constructing a mixed state decomposition filter by using the center region.
7. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 6, characterized in that, The image position matrix in S210 is expressed as: （7）； wherein , , , denotes a low resolution image; The index of any low-resolution image in the image position matrix in S220 is expressed as: （8）； The index of the two symmetric images in the image position matrix in S220 is expressed as （9）； wherein denotes a symmetric image an index in the image position matrix, denotes a symmetric image an index in the image position matrix; The center region coordinates in S230 are expressed as: （10）； The center region in S230 is expressed as: （11）； The mixed state decomposition filter in S240 is expressed as: （12）； wherein, , denote the elements of the matrix , the two indices corresponding to the row and column of the element, , , is an empirical constant between 0 and 1, is the number of images of the central region.
8. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 7, characterized in that, The coherence enhanced image in S300 is expressed by the formula: （13）； wherein denotes a matrix composed of all low resolution images, denotes a mixed state decomposition filter, denotes a coherence-enhanced image; The high-resolution spectrum in S400 is expressed by the formula: （14）； In the formula, denotes a spatial domain coordinate; The optimization function in S500 is expressed by the formula: （15）； wherein indicates a low resolution image acquired at the sampling position at the sampling position.
9. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 8, characterized in that, S600 comprises: S610, for each low-resolution image, calculate the low-resolution light field corresponding to the low-resolution image by using the high-resolution spectrum and the transfer function corresponding to the low-resolution image; S620, extract the enhanced image corresponding to each low-resolution image from the coherence-enhanced image; S630, for each low-resolution image, replace the low-resolution light field corresponding to the low-resolution image by using the enhanced image to obtain the replaced light field; S640, for each low-resolution image, transform the replaced light field to the frequency domain to obtain the light field in the frequency domain; S650, for each low-resolution image, update the low-resolution spectrum corresponding to the low-resolution image in the high-resolution spectrum by using the light field in the frequency domain to obtain the updated high-resolution spectrum; S660, repeat S610 to S650 to obtain the updated high-resolution spectrum when the optimization function is minimum; S670, Fourier transform the updated high-resolution spectrum when the optimization function is minimum to obtain the high-resolution image.
10. The non-coherent super-resolution imaging method based on mixed decomposition according to claim 9, characterized in that, In S610, the low-resolution light field is represented by the formula: （16）； In the formula, denotes a low-resolution light field; In S630, the replaced light field is represented by the formula: （17）； wherein represents the replaced light field, represents the enhanced image; In S650, the updated high-resolution spectrum is represented by the formula: （18）； wherein is a step parameter for the update, denotes a complex conjugate operation.