CN106875338B - Image super-resolution processing method based on group sparse processing - Google Patents

Image super-resolution processing method based on group sparse processing Download PDF

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CN106875338B
CN106875338B CN201710084744.XA CN201710084744A CN106875338B CN 106875338 B CN106875338 B CN 106875338B CN 201710084744 A CN201710084744 A CN 201710084744A CN 106875338 B CN106875338 B CN 106875338B
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CN106875338A (en
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张永兵
崔泽
王好谦
王兴政
戴琼海
武景欣
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Shenzhen Weilai Media Technology Research Institute
Shenzhen Graduate School Tsinghua University
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Shenzhen Graduate School Tsinghua University
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Abstract

An image super-resolution processing method based on group sparse processing comprises the following steps: a1 obtaining low-resolution images g corresponding to different angles of illumination obtained by lighting different LED lamps in an LED array one by using an FPM platform imaging devicei(x, y); a2: obtaining a high-resolution image S of a corresponding sample from the low-resolution image through iteration and constraint conditions in a real domain and a frequency domaing(ii) a A3: obtaining the amplitude matrix of the high-resolution image, partitioning the amplitude matrix, establishing a group dictionary according to the similarity of blocks, adding sparse constraint in the image reconstruction process according to the dictionary, and obtaining the amplitude matrix Z of the high-resolution image subjected to sparse processinggam(ii) a A4: will ZgamPhase matrix Z before multiplicationgphObtaining an intermediate variable ZgS is expressed as the Lagrangian product during normal FPM iterationgAnd ZgAnd introducing the difference value to obtain the final recovered high-resolution image. The image super-resolution processing method can recover more image detail information and prevent the overfitting phenomenon of the acquired low-resolution image with errors in the image recovery process.

Description

Image super-resolution processing method based on group sparse processing
Technical Field
The invention mainly belongs to the field of microscopic imaging, and particularly relates to an image super-resolution processing method based on group sparse processing.
Background
FPM (Fourier Ptychographic Microcopy) is an emerging computational imaging method which breaks through the limitation of a traditional optical system in the aspects of space bandwidth product (the space bandwidth product determines the minimum pixel number of an image which needs to be resolved, and the limitation of the image on the selection and the balance between the resolution and a visual field range), and the method generates an image with both wide field and high resolution by utilizing the iterative combination of low-resolution images acquired under different angle illumination conditions. The FPM integrates the phase recovery principle and the synthetic aperture idea, and records a low-resolution sampling image passing through an objective lens with low digital aperture at the illumination angle of each coherent light source, and the coherent transfer function of the objective lens imposes a strict constraint on the frequency domain: the movement of the constraint in the frequency domain directly reflects the change of the illumination angle of the related light; the FPM alternately defines an amplitude match to the acquired sequence of low resolution images and a spectrum match to the moving Fourier constraint to produce a high resolution image. Compared with other methods for obtaining a high space bandwidth product, the FPM is simple, easy to adjust and operate, low in cost (only one LED matrix for controlling the lighting sequence in a programmable mode is needed to be added on the basis of original equipment), and stable in effect.
Different from the traditional block sparse image reconstruction method, the group sparse image representation reconstruction method combines the inherent local sparsity and the global similarity of the image, and the complexity and the calculation amount of the algorithm are obviously reduced while the quality of the reconstructed image is ensured.
The traditional FPM algorithm utilizes a phase recovery principle and a synthetic aperture thought, low-resolution images acquired by experiments under different illumination conditions are subjected to iteration to obtain high-resolution images, and errors in the acquisition process of the low-resolution images, such as uneven brightness of different LEDs, phase difference of synthetic apertures and the like in the experiment process are introduced into a finally recovered high-resolution image matrix while the information of each low-resolution image is fully utilized.
Disclosure of Invention
The invention mainly aims to provide an image super-resolution processing method based on group sparse processing, aiming at the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
an image super-resolution processing method based on group sparse processing comprises the following steps:
a1 obtaining low-resolution images g corresponding to different angles of illumination obtained by lighting different LED lamps in an LED array one by using an FPM platform imaging devicei(x,y)；
A2: the low-resolution images obtained under different angle illumination conditions are corresponding to the offset of the original sample image on the frequency domain, and the high-resolution image S of the corresponding sample is obtained from the low-resolution images through iteration and the constraint conditions of the real domain and the frequency domaing；
A3: obtaining the amplitude matrix of the high-resolution image, partitioning the amplitude matrix, establishing a group dictionary according to the similarity of blocks, adding sparse constraint in the image reconstruction process according to the dictionary, and obtaining the amplitude matrix Z of the high-resolution image subjected to sparse processinggam；
A4: will ZgamPhase matrix Z before multiplicationgphObtaining an intermediate variable ZgS is expressed as the Lagrangian product during normal FPM iterationgAnd ZgAnd introducing the difference value to obtain the final recovered high-resolution image.
Further:
step a2 includes the following steps:
a2.1: initial guess for high resolution image to be reconstructed
Figure BDA0001227022930000021
And Fourier transform is carried out on the initial guess to obtain
Figure BDA0001227022930000022
A2.2: in the high resolution image frequency domain
Figure BDA0001227022930000023
Selecting the sub-area corresponding to the lighting of the ith LED
Figure BDA0001227022930000024
Multiplying by pupil function and invertingFourier transform to obtain
Figure BDA0001227022930000025
A2.3: will be provided with
Figure BDA0001227022930000026
With acquired low-resolution images
Figure BDA0001227022930000027
Amplitude replacement to obtain new low-resolution image
Figure BDA0001227022930000028
A2.4: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure BDA0001227022930000029
By using
Figure BDA00012270229300000210
Replacing corresponding sub-regions in a high resolution image
Figure BDA00012270229300000211
A2.5: repeating the operation A2.2-A2.4 on the data acquired under the condition of the illumination of the rest other LEDs;
wherein the content of the first and second substances,
Figure BDA00012270229300000212
respectively the amplitude and the phase of the high-resolution image to be reconstructed;
Fh,
Figure BDA00012270229300000213
respectively the amplitude and the phase of the high-resolution image in the frequency domain;
Fsub,
Figure BDA00012270229300000214
respectively for the intercepted high resolution imageThe amplitude and phase of a certain sub-region in the frequency domain;
Figure BDA00012270229300000215
respectively the amplitude and phase of a sub-region of the intercepted high-resolution image in the real domain
Figure BDA00012270229300000216
In real field for the collected low resolution images corresponding to the ith LED on the FPM experimental platform
Amplitude and phase;
Fm,
Figure BDA00012270229300000217
respectively the amplitude and the phase of the low-resolution image subjected to amplitude replacement in the frequency domain;
the iteration is repeated to obtain a high-resolution image.
In step a2, the whole iteration process is carried out for a plurality of times until the following conditions are met:
Figure BDA00012270229300000218
wherein
Figure BDA00012270229300000219
The image is a low-resolution image acquired under the lighting condition of the ith LED;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresenting the spatial angular variation, i.e. the offset, of the resulting image under the ith LED illumination condition.
The method for obtaining the high-resolution image amplitude matrix subjected to the sparse processing in the step A3 comprises the following steps: the method comprises the steps of partitioning an input image representation matrix into blocks according to a certain step length, an overlapping rate and a block size, searching a plurality of blocks matched with a certain block in a matrix setting range according to Euclidean distance to form a group, changing a dictionary with the blocks as basic units into a dictionary with the groups as units, performing sparse constraint on group representation vectors in the dictionary corresponding to each block in the process of reconstructing an image according to the dictionary, and finally utilizing a high-resolution matrix reconstructed by the groups, namely the matrix with sparse properties.
In step a4, introducing an FPM algorithm to the sparse high resolution matrix as the intermediate variable, intercepting a subregion corresponding to a certain LED illumination in the high resolution image matrix in step a2.2, intercepting subregions at the same position as the sparse high resolution matrix of the intermediate variable, taking a difference between the intercepted sparse high resolution matrix and two subregions of the high resolution matrix and multiplying by a lagrangian product, and then multiplying by the lagrangian product in step a2.4
Figure BDA0001227022930000031
Adding to replace in a high resolution image matrix
Figure BDA0001227022930000032
And the corresponding sub-area applies the above mode to the condition of remaining other LED illumination, namely, an intermediate variable is introduced into the FPM iteration process.
In step a1, the FPM platform should include a microscope with a built-in imaging device and a programmable LED array, the distance between adjacent LEDs is fixed, and the distance between the LED array and the stage is fixed; the variation offset of the image obtained under different angle illumination conditions in the spatial angle is as follows:
Figure BDA0001227022930000033
where τ represents the wavelength of light emitted by the LED and (x)c，yc) Representing the position coordinates of the central LED in the entire LED matrix, (x)i，yi) Represents the position coordinates of a certain LED including the central LED in the whole LED matrix, and h represents the distance between the LED matrix and the object stage.
The radius of the synthetic aperture is
Figure BDA0001227022930000034
Wherein radius represents the numerical aperture of the objective lens in the FPM stage, and τ represents the wavelength of the emitted light; the synthetic aperture is represented in the frequency domain as the radius of the pupil function.
In step A1, the LED matrix is arranged in a square matrix or concentric circle, preferably, the distance between adjacent LEDs is 4mm, and the distance between the LED array and the stage is fixed to 7-8 cm.
In step a4, the iterative process of the FPM includes:
a4.1: in the frequency domain of the high-resolution image to be restored
Figure BDA0001227022930000035
Intercepting sub-area corresponding to ith LED illumination
Figure BDA0001227022930000041
Multiplying the selected sub-region by the pupil function, and performing inverse Fourier transform to obtain
Figure BDA0001227022930000042
Intercepting intermediate variables Z simultaneouslygOf the same sub-region
Figure BDA0001227022930000043
A4.2: will be provided with
Figure BDA0001227022930000044
With low resolution images of the corresponding LEDs acquired
Figure BDA0001227022930000045
Amplitude replacement to obtain new low-resolution image
Figure BDA0001227022930000046
A4.3: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure BDA0001227022930000047
Will be provided with
Figure BDA0001227022930000048
Sub-region corresponding to intermediate variable
Figure BDA0001227022930000049
Is obtained by subtracting and multiplying a Lagrange coefficient
Figure BDA00012270229300000410
By using
Figure BDA00012270229300000411
And SgAnd ZgReplaces the corresponding sub-region in the high resolution image frequency domain by the sum of the differences of
Figure BDA00012270229300000412
A4.4: and (4) repeating the operation of the steps 4.1-4.3 on the data acquired under the condition of the rest of other LED lights, and obtaining the high-resolution image matrix with the sparse characteristic to be recovered after the sub-region processing and replacement under all the LED lights are completed.
In step a4, the whole iteration process is performed for a plurality of times until:
Figure BDA00012270229300000413
wherein
Figure BDA00012270229300000414
The image is a low-resolution image acquired under the lighting condition of the ith LED;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresents the ith LEAnd D, the change of the image obtained under the illumination condition in the space angle is the offset.
The intermediate variables are temporarily set to a matrix of 0's for the same size elements at the first iteration.
The invention has the beneficial effects that:
the invention improves the traditional FPM algorithm, provides an image super-resolution reconstruction method based on group sparse processing and an FPM algorithm, adds a sparse constraint item of a high-resolution image to be reconstructed in the phase recovery process, prevents the overfitting phenomenon of the image reconstruction process to acquired data, and simultaneously adds some image properties which we want to the reconstructed high-resolution image. Regular term sparse constraint is added into a normal FPM algorithm, more detail information is recovered, noise control of the recovered high-resolution image surface can be realized by adjusting an error estimation coefficient in an image block reconstruction process, and an overfitting phenomenon of an acquired low-resolution image with an error in the image recovery process is prevented.
Drawings
FIG. 1 is a flowchart of an image super-resolution processing method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an FPM experiment according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.
Referring to fig. 1, in an embodiment, an image super-resolution processing method based on group sparse processing includes the following steps:
a1 obtaining low-resolution images g corresponding to different angles of illumination obtained by lighting different LED lamps in an LED array one by using an FPM platform imaging devicei(x,y)；
A2: the low resolution images obtained under different angle illumination conditions, corresponding to the offset of the original sample image in the frequency domain, can use the phase recovery algorithm and synthetic aperture concept, and use these low resolution images through iteration and in the real domain and frequencyThe constraint of the domain results in a high resolution image S of the corresponding sampleg；
A3: obtaining an amplitude matrix of the high-resolution image, partitioning the amplitude matrix, establishing a group dictionary according to block similarity, adding sparse constraint in an image reconstruction process according to the dictionary, and obtaining a high-resolution image amplitude matrix Z subjected to sparse processinggam；
A4: will ZgamPhase matrix Z before multiplicationgphObtaining an intermediate variable ZgS is expressed as the Lagrangian product during normal FPM iterationgAnd ZgAnd introducing the difference value to obtain the final recovered high-resolution image.
In a preferred embodiment, step A2 includes the steps of:
a2.1: initial guess for high resolution image to be reconstructed
Figure BDA0001227022930000051
And Fourier transform is carried out on the initial guess to obtain
Figure BDA0001227022930000052
A2.2: in the high resolution image frequency domain
Figure BDA0001227022930000053
Selecting a sub-area corresponding to the illumination of a certain LED (assuming the ith LED)
Figure BDA0001227022930000054
Multiplying by pupil function and performing inverse Fourier transform to obtain
Figure BDA0001227022930000055
A2.3: will be provided with
Figure BDA0001227022930000056
With acquired low-resolution images
Figure BDA0001227022930000057
Amplitude replacement to obtain new low-resolution image
Figure BDA0001227022930000058
A2.4: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure BDA0001227022930000059
By using
Figure BDA00012270229300000510
Replacing corresponding sub-regions in a high resolution image
Figure BDA00012270229300000511
A2.5: repeating the operation A2.2-A2.4 on the data acquired under the condition of the illumination of the rest other LEDs;
wherein the content of the first and second substances,
Figure BDA00012270229300000512
the amplitude and the phase of the high-resolution image to be reconstructed are respectively obtained, and the initial guess of the high-resolution image in a real domain is generally obtained by sampling any one of the low-resolution images acquired by the FPM experimental platform;
Fh,
Figure BDA00012270229300000513
respectively the amplitude and the phase of the high-resolution image in the frequency domain;
Fsub,
Figure BDA00012270229300000514
respectively obtaining the amplitude and the phase of a certain subregion of the intercepted high-resolution image in a frequency domain;
Figure BDA00012270229300000515
respectively the amplitude and phase of a sub-region of the intercepted high-resolution image in the real domain
Figure BDA00012270229300000516
In real field for the collected low resolution images corresponding to the ith LED on the FPM experimental platform
Amplitude and phase;
Fm,
Figure BDA00012270229300000517
respectively the amplitude and the phase of the low-resolution image subjected to amplitude replacement in the frequency domain;
the iterative operation can be repeated to obtain a high-resolution image, and the invention can be applied to FPM calculation
The conditions in the method are not limited to the above-exemplified FPM platform calculation method.
In a particularly preferred embodiment, the entire iterative process is performed a plurality of times in step a2 until:
Figure BDA0001227022930000061
wherein
Figure BDA0001227022930000062
The image is a low-resolution image acquired under the lighting condition of the ith LED;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresenting the variation in spatial angle of the resulting image (also the image spectrum) under the ith LED illumination condition
Offset in the frequency domain) i.e. offset.
In a preferred embodiment, the method for obtaining the high-resolution image amplitude matrix subjected to the sparse processing in the step a3 includes: the method comprises the steps of partitioning an input image representation matrix into blocks according to a certain step length, an overlapping rate and a block size, searching a plurality of blocks matched with a certain block to form a group according to Euclidean distance in a matrix setting range, changing a traditional dictionary with blocks as basic units into a dictionary with groups as units, performing sparse constraint on group representation vectors in the dictionary corresponding to each block in the process of reconstructing an image according to the dictionary, and finally utilizing a high-resolution matrix reconstructed by the groups, namely the matrix with sparse properties. The present invention is not limited to the high resolution image matrix sparse processing method described above.
In a preferred embodiment, in step a4, a sparse high-resolution matrix as an intermediate variable is introduced into a conventional FPM algorithm, a subregion corresponding to a certain LED illumination in the high-resolution image matrix is intercepted in step a2.2, a subregion at the same position is also intercepted as a sparse high-resolution matrix of the intermediate variable, the intercepted sparse high-resolution matrix is subtracted from two subregions of the high-resolution matrix and multiplied by a lagrangian product, and then the product is multiplied by the product of lagrangian and the product of lag
Figure BDA0001227022930000063
Adding to replace in a high resolution image matrix
Figure BDA0001227022930000064
And the corresponding sub-area applies the above mode to the condition of remaining other LED illumination, namely, an intermediate variable is introduced into the FPM iteration process. The scope of coverage of this invention is not limited to the intermediate variable introduction methods enumerated above.
Referring to fig. 2, in a preferred embodiment, in step a1, the FPM platform should include a microscope with a built-in imaging device and a programmable LED matrix, where the LED matrix may be a square matrix or a concentric circle array, the distance between adjacent LEDs is fixed, preferably 4mm, and the distance between the LED array and the stage is fixed, preferably 7-8 cm; based on the change of the image obtained under different angle illumination conditions in the spatial angle (also the shift of the image spectrum in the frequency domain), the shift amount is:
Figure BDA0001227022930000065
wherein τ represents LEDWavelength of emitted light, (x)c，yc) Representing the position coordinates of the central LED in the entire LED matrix, (x)i，yi) Represents the position coordinates of a certain LED including the central LED in the whole LED matrix, and h represents the distance between the LED matrix and the object stage.
The radius of the synthetic aperture is
Figure BDA0001227022930000071
Wherein radius represents the numerical aperture of the objective lens in the FPM stage, and τ represents the wavelength of the emitted light; the synthetic aperture is represented in the frequency domain as the radius of the pupil function.
In a preferred embodiment, in step a4, the iterative process of FPM includes:
a4.1: in the frequency domain of the high-resolution image to be restored
Figure BDA0001227022930000072
Intercept a sub-region corresponding to the illumination of a certain LED (assumed as the ith LED)
Figure BDA0001227022930000073
Multiplying the selected sub-region by the pupil function, and performing inverse Fourier transform to obtain
Figure BDA0001227022930000074
Intercepting intermediate variables Z simultaneouslygOf the same sub-region
Figure BDA0001227022930000075
A4.2: will be provided with
Figure BDA0001227022930000076
With low resolution images of the corresponding LEDs acquired
Figure BDA0001227022930000077
Amplitude replacement to obtain new low-resolution image
Figure BDA0001227022930000078
A4.3: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure BDA0001227022930000079
Will be provided with
Figure BDA00012270229300000710
Sub-region corresponding to intermediate variable
Figure BDA00012270229300000711
Is obtained by subtracting and multiplying a Lagrange coefficient
Figure BDA00012270229300000712
By using
Figure BDA00012270229300000713
And SgAnd ZgReplaces the corresponding sub-region in the high resolution image frequency domain by the sum of the differences of
Figure BDA00012270229300000714
A4.4: and (4) repeating the operation of the steps 4.1-4.3 on the data acquired under the condition of the rest of other LED illumination, and obtaining the high-resolution image matrix with the sparse characteristic to be recovered after the sub-region processing and replacement under all the LED illumination conditions are completed. Because the acquired low-resolution image information and the intermediate variable high-resolution image information with the sparse characteristic cannot be fully fused into the high-resolution matrix to be reconstructed by one time of the process, the whole iterative process needs to be carried out for many times until the following iteration stop conditions are met
Figure BDA00012270229300000715
Wherein
Figure BDA00012270229300000716
Under the lighting condition of the ith LEDA collected low resolution image;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresents the change (also the shift of the image spectrum in the frequency domain) in the spatial angle, i.e. the shift amount, of the obtained image under the ith LED illumination condition.
In the first iteration, because the original high-resolution image which needs to be substituted into the group sparse processing program is not generated, the intermediate variable is temporarily set to be a matrix with 0 elements in the same size, and the normal traditional FPM iteration process cannot be influenced.
The foregoing is a more detailed description of the invention in connection with specific/preferred embodiments and is not intended to limit the practice of the invention to those descriptions. It will be apparent to those skilled in the art that various substitutions and modifications can be made to the described embodiments without departing from the spirit of the invention, and these substitutions and modifications should be considered to fall within the scope of the invention.

Claims (9)

1. An image super-resolution processing method based on group sparse processing is characterized by comprising the following steps:
a1: acquiring corresponding low-resolution images g under different angles of illumination obtained by lighting different LED lamps in an LED array one by using an FPM platform imaging devicei(x，y)；
A2: the low-resolution images obtained under different angle illumination conditions correspond to the offset of the original sample image on the frequency domain, and the low-resolution images are subjected to iteration and the constraint conditions of the real domain and the frequency domain to obtain the high-resolution image S of the corresponding sampleg；
A3: obtaining the amplitude matrix of the high-resolution image, partitioning the amplitude matrix, establishing a group dictionary according to the similarity of blocks, and adding the group dictionary in the process of reconstructing the image according to the dictionarySparse constraint to obtain a high-resolution image amplitude matrix Z subjected to sparse processinggam；
A4: will ZgamPhase matrix Z before multiplicationgphObtaining an intermediate variable ZgS is expressed as the Lagrangian product during normal FPM iterationgAnd ZgIntroducing the difference value to obtain a finally recovered high-resolution image;
in step a4, the iterative process of the FPM includes:
a4.1: in the frequency domain of the high-resolution image to be restored
Figure FDA0002409989960000011
Intercepting sub-area corresponding to ith LED illumination
Figure FDA0002409989960000012
Multiplying the selected sub-region by the pupil function, and performing inverse Fourier transform to obtain
Figure FDA0002409989960000013
Intercepting intermediate variables Z simultaneouslygCorresponding sub-region of
Figure FDA0002409989960000014
A4.2: will be provided with
Figure FDA0002409989960000015
With low resolution images of the corresponding LEDs acquired
Figure FDA0002409989960000016
Amplitude replacement to obtain new low-resolution image
Figure FDA0002409989960000017
A4.3: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure FDA0002409989960000018
Will be provided with
Figure FDA0002409989960000019
Sub-region corresponding to intermediate variable
Figure FDA00024099899600000110
Is obtained by subtracting and multiplying a Lagrange coefficient
Figure FDA00024099899600000111
By using
Figure FDA00024099899600000112
And SgAnd ZgReplaces the corresponding sub-region in the high resolution image frequency domain by the sum of the differences of
Figure FDA00024099899600000113
A4.4: repeating the operation of the step 4.1-4.3 on the data acquired under the condition of the rest of other LEDs, and obtaining a high-resolution image matrix with sparse characteristics to be recovered after the sub-region processing and replacement under all the LED illumination conditions are completed;
Figure FDA00024099899600000114
respectively the amplitude and the phase of the high-resolution image in the frequency domain;
Figure FDA00024099899600000115
respectively obtaining the amplitude and the phase of a certain subregion of the intercepted high-resolution image in a frequency domain;
Figure FDA00024099899600000116
respectively obtaining the amplitude and the phase of a certain sub-region of the intercepted high-resolution image in a real domain;
Figure FDA00024099899600000117
respectively corresponding to the amplitude and the phase of the collected low-resolution image of the ith LED on the FPM experiment platform in a real domain;
Figure FDA00024099899600000118
the amplitude and the phase of the low-resolution image subjected to amplitude replacement in the frequency domain are respectively.
2. The method of claim 1, wherein step a2 includes the steps of:
a2.1: initial guess for high resolution image to be reconstructed
Figure FDA0002409989960000021
And Fourier transform is carried out on the initial guess to obtain
Figure FDA0002409989960000022
A2.2: in the high resolution image frequency domain
Figure FDA0002409989960000023
Selecting the sub-area corresponding to the lighting of the ith LED
Figure FDA0002409989960000024
Multiplying by pupil function and performing inverse Fourier transform to obtain
Figure FDA0002409989960000025
A2.3: will be provided with
Figure FDA0002409989960000026
With acquired low-resolution images
Figure FDA0002409989960000027
Amplitude of the waveReplacing to obtain a new low resolution image
Figure FDA0002409989960000028
A2.4: fourier transform is carried out on the newly obtained low-resolution image to obtain
Figure FDA0002409989960000029
By using
Figure FDA00024099899600000210
Replacing corresponding sub-regions in a high resolution image
Figure FDA00024099899600000211
A2.5: repeating the operation A2.2-A2.4 on the data acquired under the condition of the illumination of the rest other LEDs;
wherein the content of the first and second substances,
Figure FDA00024099899600000212
respectively the amplitude and the phase of the high-resolution image to be reconstructed;
the iteration is repeated to obtain a high-resolution image.
3. The method of claim 2, wherein the entire iterative process is performed a plurality of times in step a2 until:
Figure FDA00024099899600000213
wherein
Figure FDA00024099899600000214
The image is a low-resolution image acquired under the lighting condition of the ith LED;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresenting the spatial angular variation, i.e. the offset, of the resulting image under the ith LED illumination condition.
4. The method as claimed in claim 1, wherein the obtaining method of the high resolution image amplitude matrix subjected to the sparse processing in the step a3 comprises: the method comprises the steps of partitioning an input image representation matrix into blocks according to a certain step length, an overlapping rate and a block size, searching a plurality of blocks matched with a certain block in a matrix setting range according to Euclidean distance to form a group, changing a dictionary with the blocks as basic units into a dictionary with the groups as units, performing sparse constraint on group representation vectors in the dictionary corresponding to each block in the process of reconstructing an image according to the dictionary, and finally utilizing a high-resolution matrix reconstructed by the groups, namely the matrix with sparse properties.
5. The method as claimed in claim 2, wherein in step a4, the FPM algorithm is introduced as the sparse high resolution matrix of the intermediate variable, the sub-region corresponding to a certain LED illumination in the high resolution image matrix is intercepted in step a2.2, the sub-region at the same position is also intercepted as the sparse high resolution matrix of the intermediate variable, the intercepted sparse high resolution matrix is differenced with the two sub-regions of the high resolution matrix and multiplied by a lagrangian product, and then the difference is multiplied with the lagrangian product in step a2.4
Figure FDA0002409989960000031
Adding to replace in a high resolution image matrix
Figure FDA0002409989960000032
And the corresponding sub-area applies the above mode to the condition of remaining other LED illumination, namely, an intermediate variable is introduced into the FPM iteration process.
6. The method of claim 1, wherein in step a1, the FPM stage comprises a microscope with an imaging device built in, a programmable LED array, with a fixed distance between adjacent LEDs, and a fixed distance between the LED array and the stage; the variation offset of the image obtained under different angle illumination conditions in the spatial angle is as follows:
Figure FDA0002409989960000033
wherein λ represents the wavelength of light emitted by the LED, (x)c，yc) Representing the position coordinates of the central LED in the entire LED matrix, (x)i，yi) Representing the position coordinates of a certain LED including a central LED in the whole LED matrix, and h represents the distance between the LED matrix and the objective table;
the radius of the synthetic aperture is
Figure FDA0002409989960000034
Wherein radius represents the numerical aperture of the objective lens in the FPM platform; the synthetic aperture is represented in the frequency domain as the radius of the pupil function.
7. The method of claim 1, wherein in step A1, the LED matrix is arranged in a square matrix or concentric circles, the distance between adjacent LEDs is 4mm, and the distance between the LED array and the stage is fixed to 7-8 cm.
8. The method of claim 1, wherein in step a4, the whole iterative process is performed for a plurality of times until:
Figure FDA0002409989960000035
wherein
Figure FDA0002409989960000036
The image is a low-resolution image acquired under the lighting condition of the ith LED;
F-1representing an inverse fourier transform;
sg (k) represents the frequency domain of the high resolution image to be finally restored;
pupil stands for synthetic aperture, i.e., Pupil function;
kirepresenting the spatial angular variation, i.e. the offset, of the resulting image under the ith LED illumination condition.
9. The method of claim 1, wherein the intermediate variables are temporarily set to a matrix of 0's for the same size elements at the first iteration.
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