CN104346780B - Phase-diversity-based blind deconvolution image restoration method - Google Patents
Phase-diversity-based blind deconvolution image restoration method Download PDFInfo
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Abstract
The invention discloses a phase-diversity-based blind deconvolution image restoration method, and relates to the field of digital image processing in space remote sensing imaging systems. The problem of incapability of improving the quality of an image due to limited image quality improvement space in a conventional image restoration method is solved. The method comprises the following steps of constructing an optical imaging system, constructing a blind deconvolution minimization model by virtue of at least one acquired in-focus image and at least one acquired out-of-focus image, and decomposing the constructed blind deconvolution minimization model into image optimization and solution to two iterative sub-problems of point spread function optimization to finish image restoration. According to the method, a phase diversity method and image blind deconvolution are combined, a multi-frame image and a phase shifting technology are used for realizing image restoration, the imaging quality of an optical imaging system with wave-front aberration disturbance is comprehensively optimized, the influence of dynamic environmental aberration disturbance on the imaging quality of the optical imaging system can be compensated, and the method is large in image quality improvement space and high in robustness, and has broad application prospect and high value.
Description
Technical field
The present invention relates to the digital image processing techniques field in spatial remotely sensed imaging system is and in particular to a kind of be based on position
Mutually different blind deconvolution image recovery method.
Background technology
With the development of space remote sensing technology, to remote-sensing imaging system as matter is put forward higher requirement, but have very
Multifactor cause image quality decline.It is very fuzzy, to follow-up phase that the presence of atmospheric turbulance makes the picture qualitative change of remote sensing images obtain
Target identification and deduction cause very big difficulty;When camera is imaged on a surface target, quivering due to platform within the time for exposure
Shake and between image device and object, there is relative motion, produce as moving, take that come is image after motion blur;Sparse aperture
Optical system is capable of Space Remote Sensors lightweight and breaks through the restriction to resolution ratio for the system bore, but its packing ratio is little
In 1, the features such as the image of acquisition has intermediate frequency component damages, contrast is low, influence of noise is serious, also exist more sensitive
Piston and the sub- mirror unit that brings of heeling error not " position phase altogether " problem, also can seriously reduce the image quality of optical system.
Solving these problems mainly has following two methods:A kind of method is to be mended by Wavefront sensor self adaptation on hardware
Repay, but ADAPTIVE OPTICS SYSTEMS cost intensive;Another kind of method is collection image sequence, recovers figure by image processing method
Picture.Existing quality enhancement method, as Wiener Filtering restoring method as matter room for promotion limited it is therefore desirable to more sane
Image recovery method.
Content of the invention
It is limited and picture quality cannot be improved in order to solve the problems, such as the picture matter room for promotion that conventional images restoring method exists,
The present invention provides a kind of robustness the stronger blind deconvolution image recovery method mutually different based on position.
The present invention is as follows by solving the technical scheme that technical problem is adopted:
The blind deconvolution image recovery method mutually different based on position of the present invention, the condition of the method and step are as follows:
Step one, build optical imaging system
Step 2, collection one width are in burnt picture and at least one width defocused image
Object is imaged through optical imaging system, in optical imaging system, using at ideal image face
First area array CCD gathers a width in burnt picture, gathers at least one width defocused image, institute using the second area array CCD after spectroscope
State the second area array CCD not being located at ideal image face;
Step 3, based on the mutually different blind deconvolution image restoration in position
Collection in burnt picture and defocused image common K width, build blind deconvolution minimum model, as shown in formula (1):
In formula (1), x and { pkRepresent the image of parked and the point spread function of each image respectively;
D(x,{pk) represent data item, in order to ensure image consistency, as shown in formula (2):
In formula (2), γ represents scale factor, | | | |2Represent l2Norm, * represents convolution operation, { ykRepresent in burnt picture
And defocused image, wherein k ∈ 1,2,3 ..., K;
S (x) represents based on l0The improved image gradient of norm constrains, openness in order to ensure image gradient, as formula (3) institute
Show:
In formula (3), i represents pixel coordinate, h and v represents image level direction and vertical direction respectively, and ε represents gradient door
Limit,#() represents the gradient operator on correspondence direction, and sign () represents sign function, and R represents the matrix voluntarily specifying,
As shown in formula (16), z#I () represents hard decision thresholding operation, as shown in formula (8);
PD({pk) represent the constraint to point spread function for the position phase distinct methods, as shown in formula (4):
In formula (4), δ represents scale factor, YmI () represents that m width observes the fourier transform spectrum of data, YnI () represents the
N width observes the fourier transform spectrum of data, PmI () represents that m width observes the fourier transform spectrum of the point spread function of data, Pn
I () represents that the n-th width observes the fourier transform spectrum of the point spread function of data, m and n is positive integer;
Step 4, Optimized model solve
The blind deconvolution of above-mentioned structure is minimized model decomposition and optimizes two repeatedly for image optimization with to point spread function
Solved for subproblem, shown in the t+1 time iteration such as formula (5) and formula (6):
Iteration optimization formula (5) and formula (6) are until meeting the condition of convergence;
Shown in image optimization such as formula (7):
Formula (7) can be by being separately optimized x and z#I () completes to solve, first pass through hard decision gate method and update z#(i),
As shown in formula (8):
Obtain z#After (i), update x, stacked by matrix and obtain image array x, observing matrix y and point spread function
Matrix p, matrix of variables z#, P=[p]cConvolution matrix for p, G#=[#]cFor gradient operator matrix on correspondence direction,
[·]cFor cyclic convolution operator, rewrite formula (7) as follows:
Obtain formula (10) by solving to formula (9):
In formula (10), the transposition of T representing matrix, j represents iteration j;
To point spread function optimization such as formula (11) Suo Shi:
In formula (11), PkI () represents that kth width observes the fourier transform spectrum of the point spread function of data;
Because formula (11) middle position phase dissimilar parts are non-convex, therefore with the t time iteration ptFourier transform PtReplace and divide
Female part, obtains formula (12) through conversion:
To formula (12) middle position phase dissimilar parts application Parseval's theorem and ignore constant coefficient impact obtain new blind
Minimum of deconvoluting model:
In formula (13):
Formula (14) is transformed to through matrix heap poststack:
In formula (15):
Obtain formula (17) by solution is carried out to formula (16), complete image restoration:
(γXTX+δR)pj+1=γ XTy (17).
Described optical imaging system also includes:Telephotolens, accurate piezoelectric actuated line slideway, main control computer and storage
Device, described accurate piezoelectric actuated line slideway is electrically connected with spectroscope and main control computer respectively, described memory respectively with master
Control computer, the first area array CCD and the electrical connection of the second area array CCD;The light that described object sends is incident through disturbance corrugated
To telephotolens, then through telephotolens outgoing to spectroscope, it is divided into two bundle outgoing after spectroscope, respectively by the first face battle array
CCD and the second area array CCD receive image, and the image of reception is stored in memory, then are transferred to master control meter by memory
Calculation machine, is processed to the image receiving using main control computer, and the first area array CCD and the second area array CCD are located at two bundles respectively
At the ideal image face that light is formed, described main control computer can control accurate piezoelectric actuated line slideway motion it is possible to
Drive spectroscope to move simultaneously.
The invention has the beneficial effects as follows:
The present invention is based on optical remote sensing imaging analysis, and position phase distinct methods and image blind deconvolution are combined together, profit
Realize image restoration with multiple image and phase shift technology, the image quality of the optical imaging system that there is wave front aberration disturbance is entered
Go comprehensive optimization:
1 present invention achieves the fine definition of image restoration;
2nd, the present invention can compensate for dynamic environment aberration disturbance (as atmospheric turbulance disturbance, random vibration and sparse aperture system
The interference of the aberrations such as system) impact to optical imaging system image quality, such as image blurring etc., strengthen and improve optical imaging system
Image quality;
3rd, position of the present invention phase distinct methods integrate optics (hardware) and digital (software) method, comprise many
Plant element, as matter room for promotion is big;
4th, the effect is significant of the present invention and being easily achieved, robustness is good, has good application prospect and value.
Brief description
Fig. 1 is the composition structural representation of the optical imaging system in the present invention.
Fig. 2 is the degeneration being formed on the first area array CCD of collection in burnt picture.
Fig. 3 is the defocused image being formed on the second area array CCD of collection.
Fig. 4 is the schematic flow sheet of the blind deconvolution image recovery method mutually different based on position of the present invention.
Fig. 5 is original image.
Fig. 6 is to defocused image with the burnt restored image as obtaining after processing by the method for the present invention.
In figure:1st, object, 2, telephotolens, 3, spectroscope, the 4, first area array CCD, the 5, second area array CCD, 6, accurate
Piezoelectric actuated line slideway, 7, main control computer, 8, disturbance corrugated, 9, memory.
Specific embodiment
Below in conjunction with accompanying drawing, the present invention is described in further detail.
As shown in figure 4, the blind deconvolution image recovery method mutually different based on position, the condition of the method and the step of the present invention
Suddenly as follows:
First, build optical imaging system
As shown in figure 1, this optical imaging system includes:Object 1, telephotolens 2, spectroscope 3, the first area array CCD 4,
Second area array CCD 5, accurate piezoelectric actuated line slideway 6, main control computer 7 and memory 9, accurate piezoelectric actuated line slideway 6
Electrically connect with spectroscope 3 and main control computer 7 respectively, memory 9 respectively with main control computer 7, the first area array CCD 4 and second
Area array CCD 5 electrically connects, and the light that object 1 sends is incident to telephotolens 2 through disturbance corrugated 8, then through telephotolens 2
Outgoing, to spectroscope 3, is divided into two bundle outgoing after spectroscope 3, receives figure by the first area array CCD 4 and the second area array CCD 5 respectively
Picture, and the image of reception is stored in memory 9, then main control computer 7 is transferred to by memory 9, using main control computer 7
The image receiving is processed (blind deconvolution image restoration), the first area array CCD 4 and the second area array CCD 5 are located at two bundles respectively
Light formed ideal image face at, main control computer 7 accurate piezoelectric actuated line slideway 6 can be controlled to move it is possible to
When drive spectroscope 3 mobile.
Each composition component in above-mentioned optical imaging system is all using existing commercially available.
2nd, collection one width is in burnt picture and at least one width defocused image
After being transferred into optical imaging system, optical imaging system transmission function reduces the light that object 1 sends,
Image quality declines, and the first area array CCD 4 is located at ideal image face, gathers a width in burnt picture first with the first area array CCD 4
(in theory defocused image be 0), a width of collection is burnt as shown in Fig. 2 be deposited in memory 9 simultaneously;Spectroscope 3
Before the imaging surface of the first area array CCD 4, add second area array CCD 5 again after spectroscope 3, controlled by main control computer 7
Make accurate piezoelectric actuated line slideway 6 mobile, simultaneously drive spectroscope 3 so that the second area array CCD 5 is located near ideal image face
(certain wave aberration is contained in this position, usual out of focus be easier to obtain aberration), that is, drive spectroscope 3 produce displacement action it
Backward second area array CCD 5 applies small defocusing amount and makes the 2nd CCD5 not be located at ideal image face (compared to existing algorithm, to lead to
Often need the defocusing amount of a determination, but in present patent application, only need to the different image of at least two width out of focus, need not
Determine specific defocusing amount, illustrated with small defocusing amount therefore herein), after the second area array CCD 5 records phase shift
Image, obtains at least one width defocused image, and the width defocused image at least one width defocused image of collection is as shown in figure 3, simultaneously by it
It is stored in memory 9.
3rd, based on the blind deconvolution image restoration that position is mutually different
Collection in burnt picture and defocused image common K width, K >=2, build blind deconvolution minimum model, as shown in formula (1):
In formula (1), x and { pkRepresent the image of parked respectively and each image gathers in burnt picture and defocused image
Point spread function (PSF);
D(x,{pk) represent data item, in order to ensure image consistency, as shown in formula (2):
In formula (2), γ represents scale factor, | | | |2Represent l2Norm, * represents convolution operation, { ykRepresent collection
The image of different defocusing amounts i.e. burnt as (in theory, defocusing amount is 0) and defocused image (small defocusing amount), wherein k ∈ 1,2,
3 ..., K;
S (x) represents based on l0The improved image gradient of norm constrains, openness in order to ensure image gradient, as formula (3) institute
Show:
In formula (3), i represents pixel coordinate, h and v represents image level direction and vertical direction respectively, and ε represents gradient door
Limit,#() represents the gradient operator on correspondence direction, and sign () represents sign function, and R represents the matrix voluntarily specifying,
As shown in formula (16), z#I () represents hard decision thresholding operation, as shown in formula (8);
PD({pk) represent the constraint to point spread function (PSF) for the position phase distinct methods, as shown in formula (4):
In formula (4), δ represents scale factor, YmI () represents that m width observes the fourier transform spectrum of data, YnI () represents the
N width observes the fourier transform spectrum of data, PmI () represents that m width observes the Fourier transform of the point spread function (PSF) of data
Spectrum, PnI () represents that the n-th width observes the fourier transform spectrum of the point spread function (PSF) of data, m and n is positive integer.
4th, Optimized model solves
The blind deconvolution of above-mentioned structure is minimized model decomposition and optimizes two for image optimization with to point spread function (PSF)
Individual iteration subproblem is solved, shown in the t+1 time iteration such as formula (5) and formula (6):
Iteration optimization formula (5) and formula (6) are until meeting the condition of convergence.
1st, image optimization problem
Shown in image optimization problem such as formula (7):
Formula (7) can be by being separately optimized x and z#I () completes to solve, first pass through hard decision gate method and update z#(i),
As shown in formula (8):
Obtain z#After (i), update x, stacked by matrix and obtain image array x, observing matrix y and point spread function
Matrix p, matrix of variables z#, P=[p]cConvolution matrix for p, G#=[#]cFor gradient operator matrix on correspondence direction,
[·]cFor cyclic convolution operator, rewrite formula (7) as follows:
Obtain formula (10) by solving to formula (9):
In formula (10), the transposition of T representing matrix, j represents iteration j.
2nd, to point spread function optimization problem
To point spread function optimization problem such as formula (11) Suo Shi:
In formula (11), PkI () represents that kth width observes the fourier transform spectrum of the point spread function (PSF) of data;
Because formula (11) middle position phase dissimilar parts are non-convex, therefore with the t time iteration ptFourier transform PtReplace and divide
Female part, obtains formula (12) through conversion:
To formula (12) middle position phase dissimilar parts application Parseval's theorem (Parseval theorem) and ignore constant coefficient
Impact obtains new blind deconvolution and minimizes model:
In formula (13):
Formula (14) is transformed to through matrix heap poststack:
In formula (15):
Obtain formula (17) by solution is carried out to formula (16), complete image restoration, the restored image obtaining is as shown in Figure 6:
(γXTX+δR)pj+1=γ XTy (17)
By the original image shown in Fig. 5 is contrasted with restored image as shown in Figure 6:Restored image with former
There is minute differences, image edge clear in beginning image, Y-PSNR (PSNR) is high.
The Y-PSNR (PSNR) between burnt picture, defocused image and restored image of collection contrasts as shown in the table:
In burnt picture | Defocused image | Restored image | |
PSNR(db) | 19.7666 | 20.0865 | 26.0609 |
The PSNR value of restored image is more than the PSNR value in burnt picture and defocused image of collection, and this shows the side by the present invention
The image fault degree that method is restored is little, is capable of image restoration function.
Claims (2)
1. based on the mutually different blind deconvolution image recovery method in position it is characterised in that the condition of the method and step are as follows:
Step one, build optical imaging system
Step 2, collection one width are in burnt picture and at least one width defocused image
Object (1) is imaged through optical imaging system, in optical imaging system, using the at ideal image face
One area array CCD (4) gathers a width in burnt picture, using the second area array CCD (5) after spectroscope (3) gather at least one width from
Burnt picture, described second area array CCD (5) is not located at ideal image face;
Step 3, based on the mutually different blind deconvolution image restoration in position
Collection in burnt picture and defocused image common K width, build blind deconvolution minimum model, as shown in formula (1):
In formula (1), x and { pkRepresent the image of parked and the point spread function of each image respectively;
D(x,{pk) represent data item, in order to ensure image consistency, as shown in formula (2):
In formula (2), γ represents scale factor, ‖ ‖2Represent l2Norm, * represents convolution operation, { ykRepresent in burnt picture and out of focus
Picture, wherein k ∈ 1,2,3, K;
S (x) represents based on l0The improved image gradient of norm constrains, openness in order to ensure image gradient, as shown in formula (3):
In formula (3), i represents pixel coordinate, h and v represents image level direction and vertical direction respectively, and ε represents gradient thresholding,#
() represents the gradient operator on correspondence direction, and sign () represents sign function, and R represents the matrix voluntarily specifying, as formula
(16) shown in, z#I () represents hard decision thresholding operation, as shown in formula (8);
PD({pk) represent the constraint to point spread function for the position phase distinct methods, as shown in formula (4):
In formula (4), δ represents scale factor, YmI () represents that m width observes the fourier transform spectrum of data, YnI () represents the n-th width
The fourier transform spectrum of observation data, PmI () represents that m width observes the fourier transform spectrum of the point spread function of data, Pn(i)
Represent that the n-th width observes the fourier transform spectrum of the point spread function of data, m and n is positive integer;
Step 4, Optimized model solve
The blind deconvolution of above-mentioned structure is minimized model decomposition and optimizes two iteration for image optimization with to point spread function
Problem is solved, shown in the t+1 time iteration such as formula (5) and formula (6):
Iteration optimization formula (5) and formula (6) are until meeting the condition of convergence;
Shown in image optimization such as formula (7):
Formula (7) can be by being separately optimized x and z#I () completes to solve, first pass through hard decision gate method and update z#I (), as formula
(8) shown in:
Obtain z#After (i), update x, stacked by matrix and obtain image array x, observing matrix y and point spread function matrix number
P, matrix of variables z#, P=[p]cConvolution matrix for p, G#=[#]cFor gradient operator matrix, [] on correspondence directionc
For cyclic convolution operator, rewrite formula (7) as follows:
Obtain formula (10) by solving to formula (9):
In formula (10), the transposition of T representing matrix, j represents iteration j;
To point spread function optimization such as formula (11) Suo Shi:
In formula (11), PkI () represents that kth width observes the fourier transform spectrum of the point spread function of data;
Because formula (11) middle position phase dissimilar parts are non-convex, therefore with the t time iteration ptFourier transform PtReplace denominator portion
Point, obtain formula (12) through conversion:
To formula (12) middle position phase dissimilar parts application Parseval's theorem and ignore the impact of constant coefficient and obtain new blind going to roll up
Long-pending minimum model:
In formula (13):
Formula (14) is transformed to through matrix heap poststack:
In formula (15):
Obtain formula (17) by solution is carried out to formula (16), complete image restoration:
(γXTX+δR)pj+1=γ XTy (17).
2. the blind deconvolution image recovery method mutually different based on position according to claim 1 is it is characterised in that described light
Learn imaging system also to include:Telephotolens (2), accurate piezoelectric actuated line slideway (6), main control computer (7) and memory
(9), described accurate piezoelectric actuated line slideway (6) is electrically connected with spectroscope (3) and main control computer (7) respectively, described storage
Device (9) is electrically connected with main control computer (7), the first area array CCD (4) and the second area array CCD (5) respectively;Described object (1) is sent out
The light going out is incident to telephotolens (2) through disturbance corrugated (8), then through telephotolens (2) outgoing to spectroscope (3), warp
It is divided into two bundle outgoing after spectroscope (3), respectively image is received by the first area array CCD (4) and the second area array CCD (5), and will receive
Image be stored in memory (9), then main control computer (7) is transferred to by memory (9), right using main control computer (7)
The image receiving is processed, and the ideal that the first area array CCD (4) is located at the formation of two-beam line respectively with the second area array CCD (5) becomes
At image planes, described main control computer (7) can control accurate piezoelectric actuated line slideway (6) motion to divide it is possible to drive simultaneously
Light microscopic (3) is mobile.
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"A new blind deconvolution algorithm based on a gradient method with phase spectral constraints";E.Uchino et al;《Fourth International Conference on Hybrid Intelligent Systems, 2004. HIS’04》;20050404;论文第1-6页 * |
"稀疏孔径光学系统成像的图像恢复算法研究";李波;《中国优秀硕士学位论文全文数据库 信息科技辑》;20100715(第7期);论文第8-56页 * |
"稀疏孔径望远镜退化图像复原技术研究";孙敬建;《中国优秀硕士学位论文全文数据库 信息科技辑》;20120715(第7期);论文第9-60页 * |
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