CN108550108B - Fourier laminated imaging image reconstruction method based on phase iteration minimization - Google Patents
Fourier laminated imaging image reconstruction method based on phase iteration minimization Download PDFInfo
- Publication number
- CN108550108B CN108550108B CN201710898958.0A CN201710898958A CN108550108B CN 108550108 B CN108550108 B CN 108550108B CN 201710898958 A CN201710898958 A CN 201710898958A CN 108550108 B CN108550108 B CN 108550108B
- Authority
- CN
- China
- Prior art keywords
- resolution
- image
- low
- sub
- reconstruction
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformation in the plane of the image
- G06T3/40—Scaling the whole image or part thereof
- G06T3/4053—Super resolution, i.e. output image resolution higher than sensor resolution
- G06T3/4076—Super resolution, i.e. output image resolution higher than sensor resolution by iteratively correcting the provisional high resolution image using the original low-resolution image
Abstract
The invention belongs to the technical field of Fourier laminated imaging, and particularly relates to a Fourier laminated imaging image reconstruction method based on phase iteration minimization. The method comprises the following steps: s1, generating amplitude sub-images corresponding to a series of low-resolution sub-images; s2, obtaining reconstruction algorithm parameters including the position of the frequency spectrum generated by each low-resolution amplitude sub-image in the high-resolution reconstruction frequency spectrum, a pupil function and the like, and establishing the relation between the low-resolution amplitude sub-image and the high-resolution reconstruction image; s3, taking the phase restoration as one of the optimization targets, generating an optimized target function of the image reconstruction target, and solving through iterative minimization to obtain a high-resolution reconstruction image frequency spectrum; and S4, performing Fourier inversion on the frequency spectrum of the high-resolution reconstructed image, and taking the module of the result as the image after high-resolution reconstruction. The invention carries out high-resolution image reconstruction by using the same number of low-resolution sub-images, and has better reconstruction intensity image quality.
Description
Technical Field
The invention belongs to the technical field of Fourier laminated imaging, and particularly relates to a Fourier laminated imaging image reconstruction method based on phase iteration minimization.
Background
From birth of the first microscope to the present, the optical microscopic imaging technology is rapidly developed, and meanwhile, the requirements of people on image quality are higher and higher. It is desirable to obtain both high resolution images and a large field of view, however, in conventional optical imaging devices, the field of view and magnification are not compatible. The large field of view inevitably leads to insufficient magnification, and although the larger appearance of the object can be observed, the finer part of the object cannot be seen clearly; conversely, a high magnification necessarily results in an undersized field of view, which is not conducive to observing the morphology of the object. Theoretically, the resolution of the microscope can be improved by increasing the numerical aperture, but the actual effect is not particularly obvious, and the following methods are mainly used: the first method is to increase the refractive index of the working medium, and is generally implemented by injecting a liquid having a high refractive index, but there are problems in that impurities are mixed in the liquid, the liquid overflows, and the expansion and contraction are caused by heat, and the numerical aperture to be increased is considerably limited. Another method is to use a lens with a larger diopter to construct the objective lens, which is inconvenient because the focal length of the objective lens becomes shorter, resulting in a limited working distance. Other methods increase the numerical aperture by increasing the aperture of the objective lens, and the objective lens needs to be designed to correct distortion, which is very complicated.
The proposal of Fourier ptychographic microscopy (FPM for short) opens up a new pattern of imaging devices, which is significant in that: high resolution, large field of view and quantitative phase imaging. The initial experimental facility is that a square LED array is used as a light source, the LED units at each position are sequentially lightened to carry out imaging to obtain a series of sub-images with low resolution, and then all the sub-images are used for generating images with high resolution by an image reconstruction method. Because only one LED unit is lighted each time, the time consumption is long in the process of acquiring the sub-images, the data volume of the acquired sub-images is too large, and the reconstruction process is relatively slow. In addition, many unknown system errors exist in Fourier laminated imaging, such as illumination brightness inconsistency of LED units, aberration of objective lenses and the like, and the errors can affect the quality of images reconstructed by the Fourier laminated imaging. Therefore, in order to further improve the imaging performance, researchers at home and abroad propose a series of improvement methods which can be divided into two types: the first kind of improved method mainly aims at reducing the imaging time of the system, for example, Lei et al (Multiplexed coded amplification for fourier Ptychographic with an LED array micro-scope) proposes a method using composite coding, and lights up a plurality of LED units for imaging at the same time. The second kind of improved method researches a new Fourier laminated imaging image reconstruction method, thereby improving the reconstruction precision and the reconstruction resolution. For example, Bian et al propose a fourier stack imaging image reconstruction method based on Wirtinger Flow, making it possible to reconstruct high resolution images from sub-images with low signal-to-noise ratio in FPM.
The phase recovery is used as an objective function for reconstruction optimization of the Fourier laminated imaging image, so that the Fourier laminated imaging image reconstruction method based on phase iteration minimization is provided.
Disclosure of Invention
The invention provides a Fourier laminated imaging image reconstruction method based on phase iteration minimization, belongs to a Fourier laminated imaging method, solves the problem of how to effectively reconstruct a high-resolution image through a series of acquired low-resolution sub-images in Fourier laminated imaging, and can be applied to various Fourier laminated imaging systems.
The invention relates to a Fourier laminated imaging image reconstruction method based on phase iteration minimization, which specifically comprises the following steps:
step S1, generating amplitude sub-images corresponding to a series of low-resolution sub-images;
step S2, obtaining reconstruction algorithm parameters including the position of the frequency spectrum generated by each low-resolution amplitude sub-image in the high-resolution reconstruction frequency spectrum and the pupil function, and establishing the relation between the frequency spectrum of the low-resolution amplitude sub-image and the frequency spectrum of the high-resolution reconstruction image;
step S3, using the phase restoration as one of the optimization objectives, generating an objective function for image reconstruction objective optimization, and solving through iterative minimization to finally obtain a high resolution reconstructed image spectrum, which is specifically implemented as follows,
step S31, carrying out vectorization operation on the two-dimensional matrix corresponding to each low-resolution amplitude sub-image to generate a one-dimensional column vector;
in step S32, assume that the amplitude-one-dimensional column vector of the low-resolution amplitude sub-image vectorized in step S31 is represented as bi,i∈[1,L']Where L' represents the total number of low resolution amplitude sub-images and the corresponding phase-one dimensional column vector is represented as piThe low-resolution amplitude subimage corresponds to a cell in the high-resolution image spectrum denoted ziThe objective function f for optimizing the image reconstruction target is expressed as:
wherein, A (z)i)＝Vec(F-1[Mat(zi)×P]) P is a pupil function; mat (-) represents the inverse of vectorization, i.e. a one-dimensional column vector is transformed into a two-dimensional matrix, F-1(-) represents the inverse Fourier transform, Vec (·) represents the vectorization operation of a two-dimensional matrix, and indicates the dot product operation;
step S33, adopting iterative minimization algorithm to respectively aim at ziAnd piAn iterative solution is performed, as described in detail below,
k represents the number of iterations, ΔzRepresenting a gradient descent step, fzRepresents f with respect to ziThe first partial derivative,/represents a point division operation;
step S34, ΔzThe calculation was carried out using the following formula,
the min (x, y) operation represents the calculation of the minimum of x and y, umIs a threshold constant, τ0Is a proportionality constant, τ ═ k × a, a is a constant;
in step S35, based on equation (3),
the following formula can be used for calculation,
A*(·)＝Vec(F[Mat(·)]×P*)，A*is the conjugate transpose of A, P*Is a conjugate transpose matrix of P, F [. cndot.)]Represents a fourier transform;
step S36, by ziReconstruction of z, eachZ isiCorresponding to a fraction of z, let z be assumediHas a coordinate of (q) in the upper left corner of the position of the spectrum in the high-resolution reconstructed spectrum1,q2) Then, based on the relationship between the spectrum of the low-resolution-amplitude sub-image and the spectrum of the high-resolution reconstructed image in step S2, the following relationship is obtained,
Mat(z)(q1:q1+n1,q2:q2+n2)⊙L＝Mat(zi)×P (6)
wherein, Mat (z) (1: n)1,1:n2) In 1: n1Denotes from the first row to the n-th row1All pixels in a row, 1: n2Denotes from the first column to the n-th column2All pixels in the column, L represents a binary template information with a resolution equal to P, L being generated by P, L (i, j) being equal to 1 if the value P (i, j) at coordinate (i, j) is not equal to 0, otherwise L (i, j) being equal to 0;
step S37, repeating the steps S33 to S36, wherein the iteration number is T;
step S4, inverse fourier transform is performed on the high-resolution reconstructed image spectrum, and the resulting model is used as the high-resolution reconstructed image.
Then, in step S32, p is initialized according to the objective functioniSet to a one-dimensional column vector of all 0, initial ziThe value of (d) is generated by: calculate | | | bi||2,i∈[1,L]Maximum value of Q, | · | | non-woven phosphor2Represents a two-norm; calculating a frequency spectrum value q 'corresponding to q, further amplifying q' to the same size as the high-resolution image frequency spectrum, and comparing the amplified result with ziThe part corresponding to the spatial position is taken as ziIs started.
Then, in step S36, z is adjacent to ziThe spectrum of (a) has a certain overlap in the high-resolution reconstructed spectrum, the overlap is processed in the following way,
let P1 and P2 denote two adjacent Mats (z), respectively1) And Mat (z)2) Corresponding regions, assuming that P3 is in the corresponding overlapping portion of the two regions, mat (z) calculates the spectral value P (i, j) at coordinate (i, j) as follows:
(1) if (i, j) belongs to P1 but not P3, then P (i, j) is equal to the spectral value at the P1 corresponding to the coordinate (i, j);
(2) if (i, j) belongs to P2 but not P3, then P (i, j) is equal to the spectral value at the P2 corresponding to the coordinate (i, j);
(3) if (i, j) belongs to P3, then P (i, j) is equal to the sum of the spectral value at coordinate (i, j) corresponding to P1 and the spectral value at coordinate (i, j) corresponding to P2, averaged.
In step S37, the number of iterations is 100.
In step 1, a series of amplitude sub-images corresponding to the low-resolution sub-images are generated by a hardware system in the wide-field high-resolution fourier-folded imaging microscope.
Compared with the prior art, the invention has the advantages and beneficial effects that: the method comprises the steps of establishing a relation between low-resolution amplitude sub-images and high-resolution reconstructed images, then using phase recovery as one of optimization targets to generate an optimized target function of the image reconstruction target, and solving through iterative minimization, so that a reconstruction problem is converted into iterative operation of multiple steps to obtain a high-resolution reconstructed image frequency spectrum.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a relationship between a frequency spectrum of a low-resolution amplitude sub-image and a frequency spectrum of a high-resolution reconstructed image according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the weighted average method of step S36 according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a spectrum of a low-resolution amplitude sub-image for spectrum recovery and high-resolution reconstructed image according to an embodiment of the present invention;
FIG. 5 is an original high resolution intensity image of an embodiment of the present invention;
FIG. 6 is an original high resolution phase image in an embodiment of the present invention;
FIG. 7 is a simulated pupil function in example 1 of the present invention;
FIG. 8 shows the reconstruction results of embodiment 1 of the present invention, (a) a reconstructed high resolution intensity image, (b) a reconstructed high resolution phase image;
FIG. 9 is a high resolution intensity image and a high resolution phase image generated based on a WFP algorithm in an embodiment of the present invention, (a) a high resolution intensity image generated based on a WFP, and (b) a high resolution phase image generated based on a WFP;
FIG. 10 is a simulated pupil function in example 2 of the present invention;
fig. 11 shows the reconstruction results of embodiment 2 of the present invention, (a) a reconstructed high-resolution intensity image, and (b) a reconstructed high-resolution phase image.
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the embodiments.
As shown in fig. 1, the technical solution of the embodiment of the present invention can be implemented by the following steps:
s1, generating a series of amplitude sub-images corresponding to low-resolution sub-images through a hardware system in a Wide-field high-resolution Fourier transform graphical microscope (Wide-field), wherein the low-resolution sub-images can be images obtained through actual shooting and can also be generated through simulation;
the amplitude sub-images corresponding to each low-resolution sub-image have the same generation method. Assuming that the pixel intensity corresponding to the spatial coordinate (x, y) of the ith low-resolution sub-image is I (x, y), the pixel amplitude I' (x, y) corresponding to the spatial coordinate (x, y) of the corresponding amplitude sub-image is calculated as follows:
s2, obtaining reconstruction algorithm parameters including the position of a frequency spectrum generated by each low-resolution amplitude sub-image in a high-resolution reconstruction frequency spectrum and a pupil function, and establishing a relation between the low-resolution amplitude sub-images and the high-resolution reconstruction image;
assuming low resolutionThe resolution of the degree sub-image is (n)1,n2) The resolution of the reconstructed high-resolution image is (N)1,N2) The position of the spectrum generated by each low-resolution amplitude sub-image in the high-resolution reconstruction spectrum is calculated according to the spatial geometric position of the LED in the LED array corresponding to each generated sub-image, and a specific calculation method can be found in the literature (Wide-field, high-resolution Fourier transform graphical microscope, Wide-field, high-resolution folded imaging microscope), which is not described in the present invention; the pupil function is represented by a two-dimensional matrix P, which in the ideal case can be considered as a binary template. In practical application, a required pupil function can be generated by a Wide-field high-resolution Fourier transform graphical microscope (Wide-field high-resolution Fourier folded imaging microscope) method according to information such as a field angle, a magnification factor, a pixel size and the like. Taking the ith low-resolution amplitude sub-image as an example, the relationship between the spectrum G of the high-resolution reconstructed image and the spectrum F of the low-resolution amplitude sub-image is introduced. Let us assume that the position of the frequency spectrum of the ith low-resolution-amplitude sub-image in the high-resolution reconstructed frequency spectrum is at the upper-left coordinate (q)1,q2) Then, the following relationship is obtained:
G(q1:q1+n1,q2:q2+n2)⊙L＝F(1:n1,1:n2)×P (1)
wherein, F (1: n)1,1:n2) In 1: n1Denotes from the first row to the n-th row1All pixels in a row, 1: n2Denotes from the first column to the n-th column2All pixels in a column, L represents a binary template information with a resolution equal to P, L is generated by P, and if the value P (i, j) ≠ 0 at coordinate (i, j), L (i, j) ═ 1, otherwise L (i, j) ≠ 0, as shown schematically in fig. 2.
S3, using the phase restoration as one of the optimization targets to generate an optimized target function of the image reconstruction target, and solving through iterative minimization, so that the reconstruction problem is converted into iterative operation of multiple steps to solve the high-resolution reconstruction image frequency spectrum, and the method is specifically realized as follows:
s31, vectorizing each low-resolution amplitude sub-image (generated by the step S1) to generate a one-dimensional column vector, wherein the method comprises the following steps:
it is assumed that each low-resolution amplitude sub-image (two-dimensional matrix M) can be represented as
mijRepresenting the value at coordinate (i, j) in the two-dimensional matrix M, i.e. the amplitude value, M and N refer to the number of rows and columns, respectively, of the two-dimensional matrix M.
After the vectorization operation, the corresponding one-dimensional column vector M' may be represented as:
M'＝[m11,m21,…,mM1,m12,…,mM2,…,m1N,…,mMN]T
s32, assuming that the amplitude one-dimensional column vector of the low-resolution amplitude sub-image after vectorization in the step S31 is represented as bi,i∈[1,L]Where L represents the total number of low resolution amplitude sub-images and the corresponding phase-one dimensional column vector is represented as pi(initial p)iOne-dimensional column vector settable to an all-0), where biAnd piThe relationship to M' is as follows: biAnd piThe amplitude one-dimensional column vector and the phase one-dimensional column vector corresponding to the ith low-resolution amplitude sub-image are respectively. M' corresponds to M and is used to describe how to generate the required one-dimensional column vector by a two-dimensional matrix. The corresponding high resolution image spectrum has its cells denoted zi(ziAnd piSee formula (3)), according to the relation of step S2, the objective function f for optimizing the image reconstruction target can be expressed as:
wherein, A (z)i)＝Vec(F-1[Mat(zi)×P]) And P is the pupil function. Mat (-) represents the inverse of vectorization, i.e. transforming a one-dimensional column vector into a two-dimensional matrix. F-1(. generation)Table inverse fourier transform. Vec (-) represents a vectorization operation of a two-dimensional matrix. An indication of a point product operation.
Initial ziThe value of (d) can be generated by: 1) calculate | | | bi||2,i∈[1,L]Maximum value of Q, | · | | non-woven phosphor2Representing a two-norm. And calculating a spectral value q 'corresponding to q, and further amplifying the q' to the same size as the high-resolution image spectrum. Then, z is summed with the amplified resultiThe part corresponding to the spatial position is taken as ziIs started.
S33, in order to solve the formula (2), an iterative minimization algorithm is adopted for ziAnd piPerforming iterative solution, specifically as follows:
k represents the number of iterations, ΔzRepresenting a gradient descent step, fzRepresents f with respect to ziThe first partial derivative,/represents a point division operation.
S34:ΔzThe calculation can be done using the following formula:
the min (x, y) operation represents the calculation of the minimum of x and y, umIs a threshold constant, τ0For the proportionality constant, τ ═ k × a, a is constant, and the values of the relevant parameters can be obtained by the method in the literature (Phase retrieval via wirtinger flow: Theory and algorithms), in this example, u is the valuem＝0.4，τ0＝330，a＝1。
S35-based on the formula (3),
the following can be used for calculation:
A*(·)＝Vec(F[Mat(·)]×P*)，A*is the conjugate transpose of A, P*Is a conjugate transpose matrix of P, F [. cndot.)]Representing a fourier transform.
S36 from ziAnd z is reconstructed, a schematic diagram of which is shown in fig. 4. Each ziCorresponding to a fraction of z, let z be assumediHas a coordinate of (q) in the upper left corner of the position of the spectrum in the high-resolution reconstructed spectrum1,q2) Then, according to equation (1), the following relationship is obtained:
Mat(z)(q1:q1+n1,q2:q2+n2)⊙L＝Mat(zi)×P (6)
taking into account adjacent ziThere will be some overlap in the high resolution reconstructed spectrum and therefore a weighted average of the overlapping parts is required, which is schematically shown in fig. 3. Taking two regions of P1 and P2 as examples, P1 and P2 represent two adjacent Mats (z) respectively1) And Mat (z)2) Corresponding regions, assuming that P3 is in the corresponding overlapping portion of the two regions, mat (z) calculates the spectral value P (i, j) at coordinate (i, j) as follows:
(1) if (i, j) belongs to P1 but not P3, then P (i, j) is equal to the spectral value at the P1 corresponding to the coordinate (i, j);
(2) if (i, j) belongs to P2 but not P3, then P (i, j) is equal to the spectral value at the P2 corresponding to the coordinate (i, j);
(3) if (i, j) belongs to P3, then P (i, j) is equal to the spectral value at P1 corresponding to coordinate (i, j) and P2 corresponding to coordinate (i, j)
The spectral values of (a) are averaged, and in this embodiment both are given the same weight. (ii) a
And S37, repeating the steps S33 to S36, wherein the iteration number is T (T is a given constant, such as 100).
And S4, carrying out Fourier inversion on the frequency spectrum of the high-resolution reconstructed image, and taking the mode of the result as the image after the high-resolution reconstruction.
Example 1:
1. the simulation data used fig. 5 as the original high resolution intensity image X (the input is the intensity image, which is generated as a low resolution amplitude sub-image according to step S1) and fig. 6 as the original high resolution phase image Y, each at 512X 512 resolution. Constructing a simulation input high-resolution image Z ═ X (cosY + i × sinY) based on fig. 5 and fig. 6;
2. based on the Fourier laminated imaging principle, a series of low-resolution sub-images are generated through Z, the resolutions are all 64 multiplied by 64, 225 sub-images are summed, the frequency spectrum positions of the high-resolution images corresponding to the frequency spectrums of the adjacent low-resolution sub-images are overlapped in a certain area, and the number of iterations is 100;
3. the simulated pupil function is shown in fig. 7 and is 64 × 64. Centered (assuming its spatial coordinates are (m)i,mj) A circle, and radius r-26 is a radius describing a circle. The calculation procedure for the value P (x, y) at the coordinates of the pupil function (x, y) is as follows:
if it is not
Then P (x, y) is 1; otherwise, P (x, y) is 0. (ii) a
4. The reconstructed high-resolution intensity image X 'and high-resolution phase image Y' (both having a resolution of 512 × 512) are shown in fig. 8;
5. meanwhile, the simulation data is experimentally verified through a WFP algorithm (Wirtinger Flow), and the obtained high-resolution intensity image and high-resolution phase image are shown in fig. 9. Comparing fig. 8(a), fig. 9(a) and fig. 5, it can be seen that fig. 8(a) is more similar to fig. 5, fig. 9(a) is relatively blurred, and the texture and the edge are not very clear. Therefore, the method has better reconstructed image quality.
Example 2:
1. the same simulation as in example 1 was used to input a high-resolution image Z ═ X (cosY + i × sinY);
2. based on the Fourier laminated imaging principle, a series of low-resolution sub-images are generated through Z, the resolution is 128 multiplied by 128, 36 sub-images are summed, the frequency spectrum positions of the high-resolution images corresponding to the frequency spectrums of the adjacent low-resolution sub-images are overlapped in a certain area, and the number of iterations is 100;
3. simulation (Emulation)The pupil function of (a) is shown in fig. 10, and its size is 128 × 128. Centered (assuming its spatial coordinates are (m)i,mj) A circle, and radius r 51 is a radius describing a circle. The calculation procedure for the value P (x, y) at the coordinates of the pupil function (x, y) is as follows:
if it is not
Then P (x, y) is 1; otherwise, P (x, y) is 0.
4. The reconstructed high-resolution intensity image X 'and high-resolution phase image Y' (both having a resolution of 512 × 512) are shown in fig. 11. Comparing fig. 11 and fig. 9, it can be seen that the edge and the detail of the reconstructed intensity image in fig. 11 are clearer, and the reconstructed intensity image quality is better. This demonstrates that the improvement in resolution of the low resolution sub-image is beneficial to improving the reconstructed intensity image quality.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (5)
1. A Fourier laminated imaging image reconstruction method based on phase iterative minimization is characterized by comprising the following steps:
step S1, generating amplitude sub-images corresponding to a series of low-resolution sub-images;
step S2, obtaining reconstruction algorithm parameters including the position of the frequency spectrum generated by each low-resolution amplitude sub-image in the high-resolution reconstruction frequency spectrum and the pupil function, and establishing the relation between the frequency spectrum of the low-resolution amplitude sub-image and the frequency spectrum of the high-resolution reconstruction image;
step S3, using the phase restoration as one of the optimization objectives, generating an objective function for image reconstruction objective optimization, and solving through iterative minimization to finally obtain a high resolution reconstructed image spectrum, which is specifically implemented as follows,
step S31, carrying out vectorization operation on the two-dimensional matrix corresponding to each low-resolution amplitude sub-image to generate a one-dimensional column vector;
in step S32, assume that the amplitude-one-dimensional column vector of the low-resolution amplitude sub-image vectorized in step S31 is represented as bi,i∈[1,L']Where L' represents the total number of low resolution amplitude sub-images and the corresponding phase-one dimensional column vector is represented as piThe low-resolution amplitude subimage corresponds to a cell in the high-resolution image spectrum denoted ziThe objective function f for optimizing the image reconstruction target is expressed as:
wherein, A (z)i)＝Vec(F-1[Mat(zi)×P]) P is a pupil function; mat (-) represents the inverse of vectorization, i.e. a one-dimensional column vector is transformed into a two-dimensional matrix, F-1(-) represents the inverse Fourier transform, Vec (·) represents the vectorization operation of a two-dimensional matrix, and indicates the dot product operation;
step S33, adopting iterative minimization algorithm to respectively aim at ziAnd piAn iterative solution is performed, as described in detail below,
k represents the number of iterations, ΔzRepresenting a gradient descent step, fzRepresents f with respect to ziThe first partial derivative,/represents a point division operation;
step S34, ΔzThe calculation was carried out using the following formula,
the min (x, y) operation represents the calculation of the minimum of x and y, umIs a threshold constant, τ0Is a proportionality constant, τ ═ k × a, a is a constant;
step S35, baseIn the formula (3),
the following formula can be used for calculation,
A*(·)＝Vec(F[Mat(·)]×P*)，A*is the conjugate transpose of A, PIs asConjugate transpose matrix of P, F [ ·]Represents a fourier transform;
step S36, by ziReconstructing z, each ziCorresponding to a fraction of z, let z be assumediHas a coordinate of (q) in the upper left corner of the position of the spectrum in the high-resolution reconstructed spectrum1,q2) Then, based on the relationship between the spectrum of the low-resolution-amplitude sub-image and the spectrum of the high-resolution reconstructed image in step S2, the following relationship is obtained,
Mat(z)(q1:q1+n1,q2:q2+n2)⊙L＝Mat(zi)×P (6)
wherein, Mat (z) (1: n)1,1:n2) In 1: n1Denotes from the first row to the n-th row1All pixels in a row, 1: n2Denotes from the first column to the n-th column2All pixels in the column, L represents a binary template information with a resolution equal to P, L being generated by P, L (i, j) being equal to 1 if the value P (i, j) at coordinate (i, j) is not equal to 0, otherwise L (i, j) being equal to 0;
step S37, repeating the steps S33 to S36, wherein the iteration number is T;
step S4, inverse fourier transform is performed on the high-resolution reconstructed image spectrum, and the resulting model is used as the high-resolution reconstructed image.
2. The fourier stack imaging image reconstruction method based on iterative minimization of phase as claimed in claim 1, wherein: in step S32, p is initialized according to the objective functioniSet to a one-dimensional column vector of all 0, initial ziThe value of (d) is generated by: calculate | | | bi||2,i∈[1,L']Maximum value of Q, | · | | non-woven phosphor2Represents a two-norm; calculating a frequency spectrum value q 'corresponding to q, further amplifying q' to the same size as the high-resolution image frequency spectrum, and comparing the amplified result with ziThe part corresponding to the spatial position is taken as ziIs started.
3. The fourier stack imaging image reconstruction method based on iterative minimization of phase as claimed in claim 2, wherein: in step S36, z is adjacentiThe spectrum of (a) has a certain overlap in the high-resolution reconstructed spectrum, the overlap is processed in the following way,
let P1 and P2 denote two adjacent Mats (z), respectively1) And Mat (z)2) Corresponding regions, assuming that P3 is in the corresponding overlapping portion of the two regions, mat (z) calculates the spectral value P (i, j) at coordinate (i, j) as follows:
(1) if (i, j) belongs to P1 but not P3, then P (i, j) is equal to the spectral value at the P1 corresponding to the coordinate (i, j);
(2) if (i, j) belongs to P2 but not P3, then P (i, j) is equal to the spectral value at the P2 corresponding to the coordinate (i, j);
(3) if (i, j) belongs to P3, then P (i, j) is equal to the sum of the spectral value at coordinate (i, j) corresponding to P1 and the spectral value at coordinate (i, j) corresponding to P2, averaged.
4. A fourier stack imaging image reconstruction method based on iterative minimization of phase as claimed in claim 3, characterized in that: the number of iterations in step S37 is 100.
5. The Fourier stack imaging image reconstruction method based on iterative minimization of phase as claimed in claim 4, wherein: in step S1, amplitude sub-images corresponding to a series of low-resolution sub-images are generated by a hardware system in the wide-field, high-resolution fourier-folded imaging microscope.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710898958.0A CN108550108B (en) | 2017-09-28 | 2017-09-28 | Fourier laminated imaging image reconstruction method based on phase iteration minimization |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710898958.0A CN108550108B (en) | 2017-09-28 | 2017-09-28 | Fourier laminated imaging image reconstruction method based on phase iteration minimization |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108550108A CN108550108A (en) | 2018-09-18 |
| CN108550108B true CN108550108B (en) | 2020-11-03 |
Family
ID=63515706
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710898958.0A Active CN108550108B (en) | 2017-09-28 | 2017-09-28 | Fourier laminated imaging image reconstruction method based on phase iteration minimization |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108550108B (en) |
Families Citing this family (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109472842A (en) * | 2018-12-17 | 2019-03-15 | 长沙理工大学 | A kind of phase recovery imaging reconstruction method of no lens imaging |
| CN110047048B (en) * | 2019-04-17 | 2021-03-02 | 清华大学深圳研究生院 | Phase recovery improved algorithm based on MSE (mean square error) optimization |
| CN110378981B (en) * | 2019-07-19 | 2022-11-15 | 中国科学院长春光学精密机械与物理研究所 | Fourier laminated microscope pupil recovery method based on neural network |
| CN110807822B (en) * | 2019-10-14 | 2022-03-22 | 北京理工大学 | Speckle correlation imaging method and device based on Wirtinger Flow algorithm |
| CN111062889B (en) * | 2019-12-17 | 2023-10-24 | 北京理工大学 | Light intensity correction method for Fourier stacked microscopic imaging technology |
| CN111917964B (en) * | 2020-08-21 | 2022-02-01 | 青岛联合创智科技有限公司 | Lens-free fluorescent microscopic imaging device and image reconstruction method thereof |
| CN112212807B (en) * | 2020-10-14 | 2022-03-01 | 福建师范大学 | Iterative phase acceleration reading method and reading device based on single spectrum intensity image dynamic sampling |
| CN113341553B (en) * | 2021-05-27 | 2022-09-20 | 杭州电子科技大学 | Fourier laminated microscopic color imaging method |
| CN113962863B (en) * | 2021-11-01 | 2024-04-09 | 中国科学院长春光学精密机械与物理研究所 | Multi-LED multiplexing 3D-FPM reconstruction algorithm based on multilayer diffraction model |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006331901A (en) * | 2005-05-27 | 2006-12-07 | Hitachi Ltd | Observation method by phase retrieval type electron microscope |
| EP2530459A1 (en) * | 2010-01-27 | 2012-12-05 | National University Corporation Hokkaido University | Diffraction microscopy |
| CN104504654A (en) * | 2014-11-21 | 2015-04-08 | 哈尔滨工业大学 | High-resolution image reconstruction method based on directivity gradient |
| CN105225202A (en) * | 2015-09-23 | 2016-01-06 | 清华大学深圳研究生院 | A kind of method of the image super-resolution rebuilding based on FPM algorithm |
| CN105589210A (en) * | 2016-03-10 | 2016-05-18 | 中国科学院光电技术研究所 | Digital synthetic aperture imaging method based on pupil modulation |
| WO2016101008A1 (en) * | 2014-12-23 | 2016-06-30 | Canon Kabushiki Kaisha | Illumination systems and devices for fourier ptychographic imaging |
| CN106127767A (en) * | 2016-06-24 | 2016-11-16 | 南京理工大学 | A kind of method for correcting position for Fourier lamination micro-imaging technique |
| CN106371201A (en) * | 2016-11-03 | 2017-02-01 | 清华大学 | Fourier overlapping correlation imaging system and method based on computational ghost imaging |
-
2017
- 2017-09-28 CN CN201710898958.0A patent/CN108550108B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006331901A (en) * | 2005-05-27 | 2006-12-07 | Hitachi Ltd | Observation method by phase retrieval type electron microscope |
| EP2530459A1 (en) * | 2010-01-27 | 2012-12-05 | National University Corporation Hokkaido University | Diffraction microscopy |
| CN104504654A (en) * | 2014-11-21 | 2015-04-08 | 哈尔滨工业大学 | High-resolution image reconstruction method based on directivity gradient |
| WO2016101008A1 (en) * | 2014-12-23 | 2016-06-30 | Canon Kabushiki Kaisha | Illumination systems and devices for fourier ptychographic imaging |
| CN105225202A (en) * | 2015-09-23 | 2016-01-06 | 清华大学深圳研究生院 | A kind of method of the image super-resolution rebuilding based on FPM algorithm |
| CN105589210A (en) * | 2016-03-10 | 2016-05-18 | 中国科学院光电技术研究所 | Digital synthetic aperture imaging method based on pupil modulation |
| CN106127767A (en) * | 2016-06-24 | 2016-11-16 | 南京理工大学 | A kind of method for correcting position for Fourier lamination micro-imaging technique |
| CN106371201A (en) * | 2016-11-03 | 2017-02-01 | 清华大学 | Fourier overlapping correlation imaging system and method based on computational ghost imaging |
Non-Patent Citations (5)
| Title |
|---|
| "Fourier ptychographic reconstruction using Wirtinger flow optimization";Liheng Bian等;《OPTICS EXPRESS》;20150217;第23卷(第4期);第4856-4866页 * |
| "Nonlinear optimization approach for Fourier ptychographic microscopy";Yongbing Zhang等;《OPTICS EXPRESS》;20151222;第23卷(第26期);第33822-33835页 * |
| "Wide-field, high-resolution Fourier ptychographic microscopy";Guoan Zheng等;《Nat Photonics》;20130728;第7卷(第9期);第739-745页 * |
| "傅里叶叠层显微成像技术：理论、发展和应用";孙佳嵩等;《光学学报》;20161031;第36卷(第10期);第1011005-1-1011005-19页 * |
| "基于傅里叶叠层成像的光学图像加密";许文慧等;《中国科学院大学学报》;20160930;第33卷(第5期);第612-617页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108550108A (en) | 2018-09-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108550108B (en) | Fourier laminated imaging image reconstruction method based on phase iteration minimization | |
| Nguyen et al. | Deep learning approach for Fourier ptychography microscopy | |
| CN110378981B (en) | Fourier laminated microscope pupil recovery method based on neural network | |
| CN111507462B (en) | End-to-end three-dimensional medical image super-resolution reconstruction method and system | |
| CN113870433A (en) | Light field super-resolution three-dimensional reconstruction method and system | |
| CN113506222B (en) | Multi-mode image super-resolution method based on convolutional neural network | |
| CN105976315A (en) | Microscopic imaging method based on partial Fourier space | |
| CN111626927A (en) | Binocular image super-resolution method, system and device adopting parallax constraint | |
| CN112508794A (en) | Medical image super-resolution reconstruction method and system | |
| CN110490968A (en) | Based on the light field axial direction refocusing image super-resolution method for generating confrontation network | |
| CN117252761A (en) | Cross-sensor remote sensing image super-resolution enhancement method | |
| Cao et al. | Dynamic structured illumination microscopy with a neural space-time model | |
| Wu et al. | A novel perceptual loss function for single image super-resolution | |
| Li | Image super-resolution using attention based densenet with residual deconvolution | |
| Cheng et al. | Fast and lightweight network for single frame structured illumination microscopy super-resolution | |
| CN110097503A (en) | The super-resolution method returned based on neighborhood | |
| Zhang et al. | Multiplex Fourier ptychographic reconstruction with model-based neural network for Internet of Things | |
| CN113689545A (en) | 2D-to-3D end-to-end ultrasonic or CT medical image cross-modal reconstruction method | |
| Liu et al. | Densely connected stacked u-network for filament segmentation in microscopy images | |
| Wu et al. | Deep learning-based image super-resolution restoration for mobile infrared imaging system | |
| CN111325700A (en) | Multi-dimensional fusion algorithm and system based on color images | |
| CN116109768A (en) | Super-resolution imaging method and system for Fourier light field microscope | |
| Choi et al. | Group-based bi-directional recurrent wavelet neural network for efficient video super-resolution (VSR) | |
| CN113689544B (en) | Cross-view geometric constraint medical image three-dimensional reconstruction method | |
| CN113191949B (en) | Multi-scale super-resolution pathology image digitizing method, system and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |