CN108550108A - A kind of Fourier's lamination image method for reconstructing minimized based on phase iteration - Google Patents
A kind of Fourier's lamination image method for reconstructing minimized based on phase iteration Download PDFInfo
- Publication number
- CN108550108A CN108550108A CN201710898958.0A CN201710898958A CN108550108A CN 108550108 A CN108550108 A CN 108550108A CN 201710898958 A CN201710898958 A CN 201710898958A CN 108550108 A CN108550108 A CN 108550108A
- Authority
- CN
- China
- Prior art keywords
- resolution
- subgraph
- image
- fourier
- spectrum
- 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.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 38
- 238000003475 lamination Methods 0.000 title claims abstract description 25
- 238000001228 spectrum Methods 0.000 claims abstract description 75
- 238000003384 imaging method Methods 0.000 claims abstract description 21
- 210000001747 pupil Anatomy 0.000 claims abstract description 15
- 238000005457 optimization Methods 0.000 claims abstract description 14
- 238000011084 recovery Methods 0.000 claims abstract description 7
- 239000011159 matrix material Substances 0.000 claims description 19
- 230000000007 visual effect Effects 0.000 claims description 10
- 230000008569 process Effects 0.000 claims description 7
- 238000013139 quantization Methods 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 2
- 238000010586 diagram Methods 0.000 description 5
- 238000000386 microscopy Methods 0.000 description 4
- 238000007792 addition Methods 0.000 description 3
- 230000003321 amplification Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 239000007788 liquid Substances 0.000 description 3
- 238000003199 nucleic acid amplification method Methods 0.000 description 3
- 239000000243 solution Substances 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 238000005286 illumination Methods 0.000 description 2
- 230000004075 alteration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000000205 computational method Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000012535 impurity Substances 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000000399 optical microscopy Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformations in the plane of the image
- G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
- G06T3/4053—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
- G06T3/4076—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution using the original low-resolution images to iteratively correct the high-resolution images
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Image Analysis (AREA)
Abstract
The invention belongs to Fourier's lamination technical field of imaging, and in particular to a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration.Include the following steps：S1 generates a series of corresponding amplitude subgraph of low resolution subgraphs；Position of the frequency spectrum that S2, acquisition algorithm for reconstructing parameter, including every width low resolution amplitude subgraph generate in super-resolution reconstruction frequency spectrum, pupil function etc. establish the contact between low resolution amplitude subgraph and super-resolution reconstruction image；Phase recovery one of target as an optimization is generated the object function of image reconstruction objective optimization, and solved by iteration minimum, obtains super-resolution reconstruction image spectrum by S3；S4 carries out Fourier inversion, using the mould of result as the image after super-resolution reconstruction to super-resolution reconstruction image spectrum.The present invention carries out high resolution image reconstruction by equal number of low resolution subgraph, has and preferably rebuilds intensity image quality.
Description
Technical field
The invention belongs to Fourier's lamination technical field of imaging, and in particular to it is a kind of based on phase iteration minimize Fu in
Leaf lamination image method for reconstructing.
Background technology
It is born till now from First microscope, optical microscopy imaging technology is quickly grown, while people are to picture quality
Requirement it is also higher and higher.People not only wish to obtain high-resolution image, but also hope obtains big visual field, however in ordinary optical
In imaging device, visual field and amplification factor be can not both with.Big visual field necessarily causes amplification factor insufficient, although can
The larger pattern of object is observed, but the subtleer part of object can not be seen clearly；Conversely, high-amplification-factor necessarily leads to visual field mistake
It is small, it is unfavorable for observing the pattern of object.Theoretically, microscopical resolution ratio can be improved by increasing numerical aperture, but practical
Effect be not particularly evident, it is main that there are as below methods：First method is to increase the refractive index of working media, general logical
The liquid for crossing injection high refractive index realizes, but the problems of be, impurity can be mixed into liquid, liquid spilling also has
It expands with heat and contract with cold, and the numerical aperture improved is also fairly limited.Another method is come using the lens of diopter bigger
Object lens are formed, this method can so that operating distance is limited because objective focal length shortens, not very convenient.There is also pass through to increase
The mode of big objective aperture improves numerical aperture, needs to be designed also correction distortion to object lens, process is sufficiently complex.
The it is proposed of Fourier's lamination imaging technique (Fourier ptychographic microscopy, abbreviation FPM) is opened
The new frame of imaging device has been opened up, its significance lies in that：High-resolution, big visual field and quantitative phase imaging.Initial experimental facilities
It is a rectangular LED array as light source, the LED unit for lighting each position successively carries out imaging and obtains a series of low points
The subgraph of resolution, then whole subgraphs are generated into high-resolution image by image rebuilding method.Due to only lighting every time
One LED unit, it is time-consuming longer during acquiring subgraph, and also the sub-image data amount acquired is also excessively huge, weight
It is relatively slow to build process.In addition, in the imaging of Fourier's lamination, there are many unknown system errors, such as LED unit brightness of illumination
Inconsistent, object lens aberrations etc., these errors can influence the quality of Fourier's lamination imaging reconstruction image.Therefore, in order into one
Step improves its imaging performance, and domestic and international researcher proposes a series of improved methods, can be divided into two classes：First kind improvement side
Method is mainly for reducing the system imaging time, for example, (the Multiplexed coded illumination for such as Lei
Fourier Ptychography with an LED array microscope) propose the method for using composite coding, simultaneously
Light multiple LED unit imagings.The new Fourier's lamination image method for reconstructing of second class Research of Improving Method, to carry
High reconstruction accuracy and reconstruct resolution ratio.For example, Bian etc. propose it is a kind of based on Fourier's lamination of Wirtinger Flow at
As image rebuilding method, it is possibly realized so that rebuilding high-definition picture by low signal-to-noise ratio subgraph in FPM.
The present invention rebuilds the object function of optimization using phase recovery as Fourier's lamination image, to propose one kind
The Fourier's lamination image method for reconstructing minimized based on phase iteration.
Invention content
The present invention proposes a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration, belongs in Fu
Leaf lamination imaging method solves how by a series of acquired low resolution subgraphs to have in the imaging of Fourier's lamination
Effect rebuilds the problem of high-definition picture, can be applied in various Fourier's lamination imaging systems.
The present invention it is a kind of based on phase iteration minimize Fourier's lamination image method for reconstructing, specifically include as
Lower step：
Step S1 generates a series of corresponding amplitude subgraph of low resolution subgraphs；
Step S2 obtains algorithm for reconstructing parameter, including the frequency spectrum that every width low resolution amplitude subgraph generates in high-resolution
Position in rate reconstructed spectrum and pupil function establish low resolution amplitude subgraph frequency spectrum and super-resolution reconstruction image frequency
Contact between spectrum；
Phase recovery one of target as an optimization is generated the object function of image reconstruction objective optimization by step S3, and is led to
Iteration minimum is crossed to be solved, it is final to obtain super-resolution reconstruction image spectrum, it is implemented as follows,
The corresponding two-dimensional matrix of every width low resolution amplitude subgraph is carried out vectoring operations, generated one-dimensional by step S31
Column vector；
Step S32, it is assumed that one dimensional vector of low resolution amplitude subgraph amplitude after step S31 vector quantizations indicates
For bi, i ∈ [1, L], wherein L indicate that the total number of low resolution amplitude subgraph, one dimensional vector of corresponding phase are expressed as
pi, the unit that low resolution amplitude subgraph corresponds in high-definition picture frequency spectrum is expressed as zi, by image reconstruction objective optimization
Object function f be expressed as：
Wherein, A (zi)=Vec (F-1[Mat(zi) × P]), P is pupil function；The inverse mistake of Mat () representative vector
One dimensional vector is become two-dimensional matrix, F by journey-1() represents inverse Fourier transform, and Vec () represents the arrow of two-dimensional matrix
Quantization operations, ⊙ represent point multiplication operation；
Step S33 minimizes algorithm, respectively to z using iterationiAnd piIt is iterated solution, it is specific as follows,
K represents iterations, ΔzIt represents gradient and declines step-length, fzF is represented about ziFirst-order partial derivative ,/representative point removes
Operation；
Step S34, ΔzIt is calculated using following formula,
Min (x, y) operation represents the minimum value calculated in x and y, umFor threshold constant, τ0For proportionality constant, τ=k × a,
A is constant；
Step S35 is based on formula (3),Following formula calculating may be used,
A*()=Vec (F [Mat ()] × P*), A*It is the associate matrix of A, P*For the associate matrix of P, F
[] represents Fourier transformation；
Step S36, by ziRebuild z, each ziCorresponding to the part in z, it is assumed that ziFrequency spectrum super-resolution reconstruction frequency
Position top left co-ordinate in spectrum is (q1,q2), then according to low resolution amplitude subgraph frequency spectrum in step S2 and high-resolution weight
The contact between image spectrum is built, following relational expression is obtained,
Mat(z)(q1:q1+n1,q2:q2+n2) ⊙ L=Mat (zi)×P (6)
Wherein, (1 Mat (z):n1,1:n2) in 1:n1It indicates from the first row to n-th1All pixels in row, 1:n2Indicate from
First row is to n-th2All pixels in row, L represent a two-value Template Information, and resolution ratio is equal to P, and L is generated by P, if sitting
The value P (i, j) ≠ 0 at (i, j) is marked, then L (i, j)=1, otherwise, L (i, j)=0；
Step S37 repeats step S33 to step S36, iterations T；
Step S4 carries out Fourier inversion, using the mould of result as high-resolution to super-resolution reconstruction image spectrum
Image after reconstruction.
Moreover, in step S32, according to object function, initial piIt is set as a dimensional vector of a full 0, initial zi's
Value generates in the following way：Calculate | | bi||2, the maximum value q in i ∈ [1, L], | | | |2Represent two norms；Calculate q pairs
The spectrum value q' answered, further by q' be amplified to high-definition picture frequency spectrum same size, by amplified result with zi
The corresponding part in spatial position is as ziInitial value.
Moreover, in step S36, adjacent ziFrequency spectrum in super-resolution reconstruction frequency spectrum there are certain overlapping, to overlapping
Partial processing mode is as follows,
If P1 and P2 respectively represent two adjacent Mat (z1) and Mat (z2) corresponding region, it is assumed that two regions are corresponding
It is P3 in lap, then Mat (z) is as follows for spectrum value p (i, j) calculating process at (i, j) in coordinate：
(1) if (i, j) belongs to P1 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P1 respective coordinates,；
(2) if (i, j) belongs to P2 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P2 respective coordinates,；
(3) if (i, j) belongs to P3, it is the spectrum value and P2 correspondence seats at (i, j) that p (i, j), which is equal to P1 respective coordinates,
The addition of the spectrum value at (i, j) is designated as to be averaged.
Moreover, iterations are 100 in the step S37.
It is given birth to moreover, folding the hardware system in imaging microscope by wide visual field, high-resolution Fourier in the step 1
At a series of corresponding amplitude subgraph of low resolution subgraphs.
Compared with prior art, the advantages of the present invention：The method of the present invention is by establishing low resolution amplitude
Contact between subgraph and super-resolution reconstruction image generates image weight then by phase recovery one of target as an optimization
The object function of objective optimization is built, and is solved by iteration minimum, to convert Problems of Reconstruction to multiple steps
Interative computation finds out super-resolution reconstruction image spectrum, and compared with the conventional method, the present invention passes through equal number of low resolution
Rate subgraph carries out high resolution image reconstruction, has and preferably rebuilds intensity image quality.
Description of the drawings
Attached drawing 1 is flow chart of the embodiment of the present invention；
Attached drawing 2 be the embodiment of the present invention between low resolution amplitude subgraph frequency spectrum and super-resolution reconstruction image spectrum
Relation schematic diagram；
Attached drawing 3 is step S36 weighted average method schematic diagrames in the embodiment of the present invention；
Attached drawing 4 is that low resolution amplitude subgraph spectrum recovery super-resolution reconstruction image spectrum shows in the embodiment of the present invention
It is intended to；
Attached drawing 5 is original high resolution intensity image in the embodiment of the present invention；
Attached drawing 6 is original high-resolution phase image in the embodiment of the present invention；
Attached drawing 7 is the pupil function emulated in the embodiment of the present invention 1；
Reconstructed results in 8 embodiment of the present invention 1 of attached drawing, the high-resolution intensity image that (a) is rebuild, (b) high score rebuild
Resolution phase image；
High-resolution intensity image and high-resolution phase figure based on the generation of WFP algorithms in 9 embodiment of the present invention of attached drawing
Picture, the high-resolution intensity image that (a) is generated based on WFP, (b) being based on WFP generates high-resolution phase image；
Attached drawing 10 is the pupil function emulated in the embodiment of the present invention 2；
Attached drawing 11 is reconstructed results in the embodiment of the present invention 2, the high-resolution intensity image that (a) is rebuild, (b) height rebuild
Resolution phase image.
Specific implementation mode
Technical scheme of the present invention is described further with reference to the accompanying drawings and examples.
As the technical solution of Fig. 1, the embodiment of the present invention can be realized by following steps：
S1. imaging microscope (Wide-field, high-resolution are folded by wide visual field, high-resolution Fourier
Fourier ptychographic microscopy) in hardware system to generate a series of low resolution subgraphs corresponding
Amplitude subgraph, wherein low resolution subgraph can be the image that actual photographed obtains, and can also be generated by simulating；
The corresponding amplitude subgraph generation method having the same of every width low resolution subgraph.Assuming that i-th low resolution
The corresponding image pixel intensities of rate subgraph space coordinate (x, y) are I (x, y), then corresponding amplitude subgraph space coordinate (x, y)
Corresponding pixel amplitudes I'(x, y), computational methods are：
S2. algorithm for reconstructing parameter, including the frequency spectrum that every width low resolution amplitude subgraph generates are obtained in high-resolution weight
The position in frequency spectrum is built, pupil function establishes the contact between low resolution amplitude subgraph and super-resolution reconstruction image；
Assuming that the resolution ratio of low resolution amplitude subgraph is (n1,n2), the resolution ratio for rebuilding high-definition picture is (N1,
N2), wherein position of the frequency spectrum that every width low resolution amplitude subgraph generates in super-resolution reconstruction frequency spectrum is according to life
It is calculated at space geometry positions of the corresponding LED of every width subgraph in LED array, circular can be found in text
Offer (Wide-field, high-resolution Fourier ptychographic microscopy, wide visual field, high-resolution
Rate Fourier folds imaging microscope), the present invention not writes；Pupil function indicates with two-dimensional matrix P, in an ideal case
It is regarded as a binaryzation template.It can be used by information such as field angle, amplification factor, pixel dimensions in practical application
(Wide-field, high-resolution Fourier ptychographic microscopy, wide visual field, high-resolution
Fourier folds imaging microscope) the required pupil function of method generation.By taking the i-th width low resolution amplitude subgraph as an example, it is situated between
The relationship to continue between super-resolution reconstruction image spectrum G and low resolution amplitude subgraph frequency spectrum F.Assuming that the i-th width low resolution
Position top left co-ordinate of the frequency spectrum of amplitude subgraph in super-resolution reconstruction frequency spectrum is (q1,q2), then there is following relationship
Formula：
G(q1:q1+n1,q2:q2+n2) ⊙ L=F (1:n1,1:n2)×P (1)
Wherein, (1 F:n1,1:n2) in 1:n1It indicates from the first row to n-th1All pixels in row, 1:n2It indicates from first
It arranges to n-th2All pixels in row, L represent a two-value Template Information, and resolution ratio is equal to P, and L is generated by P, if coordinate
Value P (i, j) ≠ 0 at (i, j), then L (i, j)=1, otherwise, L (i, j)=0, schematic diagram is as shown in Fig. 2.
S3. by phase recovery one of target as an optimization, the object function of image reconstruction objective optimization is generated, and by repeatedly
In generation, minimizes and is solved, and to convert Problems of Reconstruction to the interative computation of multiple steps, finds out super-resolution reconstruction image
Frequency spectrum is implemented as follows：
S31:By every width low resolution amplitude subgraph (being generated by step S1) carry out vectoring operations, generate it is one-dimensional arrange to
Amount, method are as follows：
Assuming that every width low resolution amplitude subgraph (two-dimensional matrix M) can be expressed as
mijThe value at coordinate (i, j), i.e. range value in two-dimensional matrix M are represented, M and N refer respectively to the row of two-dimensional matrix M
Number and columns.
Then after vectoring operations, corresponding dimensional vector M' can be expressed as：
M'=[m11,m21,…,mM1,m12,…,mM2,…,m1N,…,mMN]T
S32:Assuming that one dimensional vector of low resolution amplitude subgraph amplitude after step S31 vector quantizations is expressed as
bi, i ∈ [1, L], wherein L indicate that the total number of low resolution amplitude subgraph, one dimensional vector of corresponding phase are expressed as pi
(initial piMay be configured as a dimensional vector of a full 0), wherein biAnd piIt is as follows with the relationship of M'：biAnd piIt is the i-th width respectively
Corresponding one dimensional vector of amplitude of low resolution amplitude subgraph and one dimensional vector of phase.M' is corresponding with M, for describing such as
What generates a required dimensional vector by two-dimensional matrix.Unit in corresponding high-definition picture frequency spectrum is expressed as zi (ziWith
piGenerating process see formula (3)), can be by the object function f of image reconstruction objective optimization according to the relational expression of step S2
It is expressed as：
Wherein, A (zi)=Vec (F-1[Mat(zi) × P]), P is pupil function.The inverse mistake of Mat () representative vector
One dimensional vector is become two-dimensional matrix by journey.F-1() represents inverse Fourier transform.Vec () represents the arrow of two-dimensional matrix
Quantization operations.⊙ represents point multiplication operation.
Initial ziValue can generate in the following way：1) calculate | | bi | |2, the maximum value q in i ∈ [1, L], | | | |2
Represent two norms.The corresponding spectrum value q' of q are calculated, are further amplified to q' and high-definition picture frequency spectrum same size.That
, by the amplified result with ziThe corresponding part in spatial position is as ziInitial value.
S33:In order to solve formula (2), algorithm is minimized using iteration, respectively to ziAnd piIt is iterated solution, specifically such as
Under：
K represents iterations, ΔzIt represents gradient and declines step-length, fzF is represented about ziFirst-order partial derivative ,/representative point removes
Operation.
S34:ΔzFollowing formula may be used to be calculated：
Min (x, y) operation represents the minimum value calculated in x and y, umFor threshold constant, τ0For proportionality constant, τ=k × a,
A is constant, and document (Phase retrieval via wirtinger flow may be used:Theory and
Algorithms the method in) carries out value, u in the present embodiment to relevant parameterm=0.4, τ0=330, a=1.
S35:Based on formula (3),Following formula calculating may be used：
A*()=Vec (F [Mat ()] × P*), A*It is the associate matrix of A, P*For the associate matrix of P, F
[] represents Fourier transformation.
S36:By ziZ is rebuild, schematic diagram is as shown in Fig. 4.Each ziCorresponding to the part in z, it is assumed that ziFrequency spectrum
Position top left co-ordinate in super-resolution reconstruction frequency spectrum is (q1,q2), then following relational expression is had according to formula (1)：
Mat(z)(q1:q1+n1,q2:q2+n2) ⊙ L=Mat (zi)×P (6)
In view of adjacent ziFrequency spectrum certain overlapping is had in super-resolution reconstruction frequency spectrum, it is therefore desirable to overlapping portion
Divide and be weighted averagely, schematic diagram is as shown in Fig. 3.Here by taking two regions P1 and P2 as an example, P1 and P2 respectively represent two
A adjacent Mat (z1) and Mat (z2) corresponding region, it is assumed that it is P3 in the corresponding lap in two regions, then Mat (z)
It is as follows for spectrum value p (i, j) calculating process at (i, j) in coordinate：
(1) if (i, j) belongs to P1 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P1 respective coordinates,；
(2) if (i, j) belongs to P2 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P2 respective coordinates,；
(3) if (i, j) belongs to P3, it is the spectrum value and P2 correspondence seats at (i, j) that p (i, j), which is equal to P1 respective coordinates,
It is designated as the addition of the spectrum value at (i, j) to be averaged, identical weight is assigned both in the present embodiment.；
S37:Step S33 to step S36 is repeated, iterations are that (T is given constant to T, such as 100).
S4. Fourier inversion is carried out to super-resolution reconstruction image spectrum, using the mould of result as super-resolution reconstruction
Image afterwards.
Embodiment 1：
1, using attached drawing 5, as original high resolution intensity image X, (input is intensity image to emulation data, according to step
S1 generates low resolution amplitude subgraph), attached drawing 6 is used as original high resolution phase image Y, and resolution ratio is 512 × 512.Base
In attached drawing 5 and the structure emulation input high-definition picture Z=X of attached drawing 6 (cosY+i × sinY)；
2, it is based on Fourier's lamination image-forming principle, a series of low resolution subgraphs are generated by Z, resolution ratio is 64 ×
64, add up to 225 subgraphs, the corresponding high-definition picture spectrum position of adjacent low resolution subgraph frequency spectrum to have certain area
Overlapping, iterations are 100 times；
3, the pupil function emulated is as shown in Fig. 7, and size is 64 × 64.With center (assuming that its space coordinate is
(mi,mj)) it is dot, radius r=26 is that radius draws circle.Pupil function coordinate was calculated for the value P (x, y) at (x, y)
Journey is as follows：
IfThen P (x, y)=1；Otherwise, P (x, y)=0.；
4, rebuild obtained high-resolution intensity image X' and high-resolution phase image Y'(resolution ratio be 512 ×
512) as shown in Fig. 8；
5 at the same by WFP algorithms (Wirtinger Flow) to above-mentioned emulation data carry out experimental verification, obtained height
Resolution intensity image and high-resolution phase image are as shown in Fig. 9.Attached drawing 8 (a), attached drawing 9 (a) and attached drawing 5 are compared, it can
To find out that attached drawing 8 (a) is more similar to attached drawing 5, attached drawing 9 (a) is comparatively fuzzy, and texture and edge are less clear.Cause
This method for the present invention has better reconstructed image quality.
Embodiment 2：
1, using emulation input high-definition picture Z=X (cosY+i × sinY) same as Example 1；
2, it is based on Fourier's lamination image-forming principle, a series of low resolution subgraphs are generated by Z, resolution ratio is 128
× 128, add up to 36 subgraphs, the corresponding high-definition picture spectrum position of adjacent low resolution subgraph frequency spectrum to have certain area
Domain is overlapped, and iterations are 100 times；
3, the pupil function emulated is as shown in Fig. 10, and size is 128 × 128.With center (assuming that its space coordinate is
(mi,mj)) it is dot, radius r=51 is that radius draws circle.Pupil function coordinate was calculated for the value P (x, y) at (x, y)
Journey is as follows：
IfThen P (x, y)=1；Otherwise, P (x, y)=0.
4, rebuild obtained high-resolution intensity image X' and high-resolution phase image Y'(resolution ratio be 512 ×
512) as shown in Fig. 11.Attached drawing 11 and attached drawing 9 are compared, it can be found that rebuilding the edge and details of intensity image in attached drawing 11
It is relatively sharp, have and preferably rebuilds intensity image quality.This illustrates that the promotion of low resolution subgraph resolution ratio is beneficial to carry
It rises and rebuilds intensity image quality.
Specific embodiment described herein is only an example for the spirit of the invention.Technology belonging to the present invention is led
The technical staff in domain can make various modifications or additions to the described embodiments or replace by a similar method
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (5)
1. a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration, which is characterized in that including as follows
Step：
Step S1 generates a series of corresponding amplitude subgraph of low resolution subgraphs；
Step S2 obtains algorithm for reconstructing parameter, including the frequency spectrum that every width low resolution amplitude subgraph generates in high-resolution weight
The position in frequency spectrum and pupil function are built, is established between low resolution amplitude subgraph frequency spectrum and super-resolution reconstruction image spectrum
Contact；
Phase recovery one of target as an optimization is generated the object function of image reconstruction objective optimization, and by repeatedly by step S3
In generation, minimizes and is solved, final to obtain super-resolution reconstruction image spectrum, is implemented as follows,
The corresponding two-dimensional matrix of every width low resolution amplitude subgraph is carried out vectoring operations by step S31, generate it is one-dimensional arrange to
Amount；
Step S32, it is assumed that one dimensional vector of low resolution amplitude subgraph amplitude after step S31 vector quantizations is expressed as bi,
I ∈ [1, L], wherein L indicate that the total number of low resolution amplitude subgraph, one dimensional vector of corresponding phase are expressed as pi, low
The unit that resolution ratio amplitude subgraph corresponds in high-definition picture frequency spectrum is expressed as zi, by the target of image reconstruction objective optimization
Function f is expressed as：
Wherein, A (zi)=Vec (F-1[Mat(zi) × P]), P is pupil function；That is, the inverse process of Mat () representative vector will
One dimensional vector becomes two-dimensional matrix, F-1() represents inverse Fourier transform, and Vec () represents the vector quantization fortune of two-dimensional matrix
It calculates, ⊙ represents point multiplication operation；
Step S33 minimizes algorithm, respectively to z using iterationiAnd piIt is iterated solution, it is specific as follows,
K represents iterations, ΔzIt represents gradient and declines step-length, fzF is represented about ziFirst-order partial derivative ,/representative point except fortune
It calculates；
Step S34, ΔzIt is calculated using following formula,
Min (x, y) operation represents the minimum value calculated in x and y, umFor threshold constant, τ0For proportionality constant, τ=k × a, a are normal
Number；
Step S35 is based on formula (3),Following formula calculating may be used,
A*()=Vec (F [Mat ()] × P*), A*It is the associate matrix of A, P*For the associate matrix of P, F [] generation
Table Fourier transformation；
Step S36, by ziRebuild z, each ziCorresponding to the part in z, it is assumed that ziFrequency spectrum in super-resolution reconstruction frequency spectrum
Position top left co-ordinate be (q1,q2), then according to low resolution amplitude subgraph frequency spectrum in step S2 and super-resolution reconstruction figure
Contact between picture frequency spectrum, obtains following relational expression,
Mat(z)(q1:q1+n1,q2:q2+n2) ⊙ L=Mat (zi)×P (6)
Wherein, (1 Mat (z):n1,1:n2) in 1:n1It indicates from the first row to n-th1All pixels in row, 1:n2It indicates from first
It arranges to n-th2All pixels in row, L represent a two-value Template Information, and resolution ratio is equal to P, and L is generated by P, if coordinate (i,
J) the value P (i, j) ≠ 0 at place, then L (i, j)=1, otherwise, L (i, j)=0；
Step S37 repeats step S33 to step S36, iterations T；
Step S4 carries out Fourier inversion, using the mould of result as super-resolution reconstruction to super-resolution reconstruction image spectrum
Image afterwards.
2. a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration as described in claim 1,
It is characterized in that：In step S32, according to object function, initial piIt is set as a dimensional vector of a full 0, initial ziValue it is logical
Under type such as is crossed to generate：Calculate | | bi||2, the maximum value q in i ∈ [1, L], | | | |2Represent two norms；Calculate the corresponding frequencies of q
Spectrum q', further by q' be amplified to high-definition picture frequency spectrum same size, by amplified result with ziSpace bit
Corresponding part is set as ziInitial value.
3. a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration as claimed in claim 2,
It is characterized in that：In step S36, adjacent ziFrequency spectrum there are certain overlappings in super-resolution reconstruction frequency spectrum, to lap
Processing mode it is as follows,
If P1 and P2 respectively represent two adjacent Mat (z1) and Mat (z2) corresponding region, it is assumed that the corresponding overlapping in two regions
It is P3 in part, then Mat (z) is as follows for spectrum value p (i, j) calculating process at (i, j) in coordinate：
(1) if (i, j) belongs to P1 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P1 respective coordinates,；
(2) if (i, j) belongs to P2 but be not belonging to P3, it is the spectrum value at (i, j) that p (i, j), which is equal to P2 respective coordinates,；
(3) if (i, j) belongs to P3, p (i, j) is equal to that P1 respective coordinates are spectrum value at (i, j) and P2 respective coordinates are
Spectrum value addition at (i, j) is averaged.
4. a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration as claimed in claim 3,
It is characterized in that：Iterations are 100 in the step S37.
5. a kind of Fourier's lamination image method for reconstructing minimized based on phase iteration as claimed in claim 4,
It is characterized in that：The hardware system in imaging microscope is folded by wide visual field, high-resolution Fourier in the step 1 and generates one
The corresponding amplitude subgraph of series of low resolution subgraph.
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 true CN108550108A (en) | 2018-09-18 |
| CN108550108B 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) |
Cited By (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 |
| CN110047048A (en) * | 2019-04-17 | 2019-07-23 | 清华大学深圳研究生院 | It is a kind of to select excellent phase recovery innovatory algorithm based on MSE |
| CN110378981A (en) * | 2019-07-19 | 2019-10-25 | 中国科学院长春光学精密机械与物理研究所 | Fourier's lamination microscope pupil restoration methods neural network based |
| CN110807822A (en) * | 2019-10-14 | 2020-02-18 | 北京理工大学 | Speckle correlation imaging method and device based on Wirtinger Flow algorithm |
| CN111062889A (en) * | 2019-12-17 | 2020-04-24 | 北京理工大学 | Light intensity correction method for Fourier laminated microscopic imaging technology |
| CN111917964A (en) * | 2020-08-21 | 2020-11-10 | 青岛联合创智科技有限公司 | Lens-free fluorescent microscopic imaging device and image reconstruction method thereof |
| CN112212807A (en) * | 2020-10-14 | 2021-01-12 | 福建师范大学 | Iterative phase acceleration reading method and reading device based on single spectrum dynamic sampling |
| CN113341553A (en) * | 2021-05-27 | 2021-09-03 | 杭州电子科技大学 | Fourier laminated microscopic color imaging method |
| CN113962863A (en) * | 2021-11-01 | 2022-01-21 | 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 |
|---|
| GUOAN ZHENG等: ""Wide-field, high-resolution Fourier ptychographic microscopy"", 《NAT PHOTONICS》 * |
| LIHENG BIAN等: ""Fourier ptychographic reconstruction using Wirtinger flow optimization"", 《OPTICS EXPRESS》 * |
| YONGBING ZHANG等: ""Nonlinear optimization approach for Fourier ptychographic microscopy"", 《OPTICS EXPRESS》 * |
| 孙佳嵩等: ""傅里叶叠层显微成像技术：理论、发展和应用"", 《光学学报》 * |
| 许文慧等: ""基于傅里叶叠层成像的光学图像加密"", 《中国科学院大学学报》 * |
Cited By (14)
| 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 |
| CN110047048A (en) * | 2019-04-17 | 2019-07-23 | 清华大学深圳研究生院 | It is a kind of to select excellent phase recovery innovatory algorithm based on MSE |
| 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 |
| CN110378981A (en) * | 2019-07-19 | 2019-10-25 | 中国科学院长春光学精密机械与物理研究所 | Fourier's lamination microscope pupil restoration methods neural network based |
| CN110807822A (en) * | 2019-10-14 | 2020-02-18 | 北京理工大学 | Speckle correlation imaging method and device based on Wirtinger Flow algorithm |
| CN111062889A (en) * | 2019-12-17 | 2020-04-24 | 北京理工大学 | Light intensity correction method for Fourier laminated microscopic imaging technology |
| CN111062889B (en) * | 2019-12-17 | 2023-10-24 | 北京理工大学 | Light intensity correction method for Fourier stacked microscopic imaging technology |
| CN111917964A (en) * | 2020-08-21 | 2020-11-10 | 青岛联合创智科技有限公司 | Lens-free fluorescent microscopic imaging device and image reconstruction method thereof |
| CN112212807A (en) * | 2020-10-14 | 2021-01-12 | 福建师范大学 | Iterative phase acceleration reading method and reading device based on single spectrum dynamic sampling |
| 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 |
| CN113341553A (en) * | 2021-05-27 | 2021-09-03 | 杭州电子科技大学 | Fourier laminated microscopic color imaging method |
| CN113962863A (en) * | 2021-11-01 | 2022-01-21 | 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 |
| 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 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108550108B (en) | 2020-11-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108550108A (en) | A kind of Fourier's lamination image method for reconstructing minimized based on phase iteration | |
| Fang et al. | Soft-edge assisted network for single image super-resolution | |
| Zhao et al. | Channel splitting network for single MR image super-resolution | |
| Huang et al. | Simultaneous super-resolution and cross-modality synthesis of 3D medical images using weakly-supervised joint convolutional sparse coding | |
| Liu et al. | Learning affinity via spatial propagation networks | |
| Lu et al. | Geometry constrained sparse coding for single image super-resolution | |
| CN117597703A (en) | Multi-scale converter for image analysis | |
| CN102831581A (en) | Method for reconstructing super-resolution image | |
| CN112508794A (en) | Medical image super-resolution reconstruction method and system | |
| Hu et al. | Recursive decomposition network for deformable image registration | |
| Wang et al. | Image super-resolution reconstruction based on generative adversarial network model with feedback and attention mechanisms | |
| Wang et al. | Group shuffle and spectral-spatial fusion for hyperspectral image super-resolution | |
| Zhou et al. | A superior image inpainting scheme using Transformer-based self-supervised attention GAN model | |
| Wu et al. | Deep learning-based image super-resolution restoration for mobile infrared imaging system | |
| Zeng et al. | Densely connected transformer with linear self-attention for lightweight image super-resolution | |
| CN116310452B (en) | Multi-view clustering method and system | |
| Li et al. | Model-informed Multi-stage Unsupervised Network for Hyperspectral Image Super-resolution | |
| CN113191367B (en) | Semantic segmentation method based on dense scale dynamic network | |
| Gao et al. | Multi-branch aware module with channel shuffle pixel-wise attention for lightweight image super-resolution | |
| CN110163800A (en) | A kind of micro- phase recovery method and apparatus of chip based on multiple image super-resolution | |
| Kapoor et al. | Multiscale metamorphic vae for 3d brain mri synthesis | |
| Xu et al. | Two-direction self-learning super-resolution propagation based on neighbor embedding | |
| CN107481196A (en) | Feature Conversion face super-resolution reconstruction method based on nearest feature line | |
| Du et al. | Mixed high-order non-local attention network for single image super-resolution | |
| Yang et al. | Depth map super-resolution via multilevel recursive guidance and progressive supervision |
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 |