CN107862655A - A kind of alternating minimization high-definition picture reconstructing method based on regularization - Google Patents
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Abstract
The invention discloses a kind of alternating minimization high-definition picture reconstructing method based on regularization, it is related to image processing field, particularly in Intelligent hardware, field of video monitoring.The present invention realizes the multiplication factor of rational rank, compensate for existing algorithm can only realize the deficiency of integer level multiplication factor according to the theory analysis that original low-resolution image sequence is carried out to secondary down-sampling.Meanwhile the limitation of existing super-resolution reconstruction color image processing is illustrated, propose to add a regular terms for including colour information in alternating minimization super-resolution reconstruction algorithm, realize the optimization processing to coloured image.
Description
Technical field
The present invention relates to image processing field, particularly in Intelligent hardware, field of video monitoring.
Background technology
Super-resolution reconstruction is one of core research contents of computer vision field, is inputted as single image or video
Image sequence, by obtaining potential information in these low-resolution images, according to algorithm model, the width of final output one is clearly
High-definition picture.Super-resolution reconstruction has a wide range of applications in many fields, such as video monitoring, remote sensing images, medical science figure
Picture, historical relic recovery etc..Many effective super-resolution reconstruction algorithms, such as the algorithm based on regularization are currently existed, but
In existing super-resolution reconstruction algorithm, picture up-sampling process and deblurring process are separated.If simply simply by oversubscription
The high-definition picture for up-sampling to obtain in resolution reconstruct carries out deblurring, then does not use sequence image in deblurring process
In advantage.Therefore, how by picture up-sampling process and deblurring process it is organic must to combine be still that a big research is challenged,
Its achievement in research also has very high application value.
The content of the invention
The present invention seeks to design a kind of base for the deficiency of the super-resolution reconstruction algorithm based on regularization to be based on canonical
The alternating minimization ultra-resolution ratio reconstructing method of change.
The present invention analyzes the deficiency of the existing super-resolution reconstruction algorithm based on regularization, for super-resolution reconstruction algorithm
Unreasonable and multiplication factor the limitation of middle solution procedure, the present invention propose that a kind of alternating minimization super-resolution reconstruction is calculated
Method.By adding a regular terms for entering row constraint to fuzzy core, upsampling process is combined with deblurring process, makes calculation
Method is more efficient；Deficiency for handling multiplication factor, propose original low-resolution image sequence carrying out secondary down-sampling, it is real
The multiplication factor of existing reason several levels；For the limitation of super-resolution reconstruction color image processing, addition one is proposed
Regular terms comprising colour information realizes effective processing to coloured image into alternating minimization super-resolution reconstruction algorithm,
The artifact that existing algorithm often occurs is different from, is more suitable for the direct observation of user.Therefore the present invention is a kind of based on regularization
Alternating minimization high-definition picture reconstructing method, this method include：
Step 1：Sequence of low resolution pictures is inputted, determines multiplication factor S, S2Less than or equal to the amount of images of input；
Step 2：If S is integer, step 4 is directly carried out；Otherwise, according to multiplication factor S, to former low-resolution image sequence
Row carry out secondary down-sampling, obtain down-sampled images；
Step 3：The down-sampled images that step 2 is obtained carry out the image registration based on mutual information；Wherein mutual information calculates
Represent that other frames and the first frame do mutual information calculating in addition to the first two field picture；
Provided with reference picture f1(x, y) and image f to be matched2(x1,y1), f1The comentropy of (x, y) is H (f1), f2(x1,
y1) comentropy be H (f2), their combination entropy is H (f1,f2), then the mutual information between themCalculation formula is：
Step 4. initializes high-definition picture and fuzzy core, and constructs a matrix fuzzy core coefficient matrix N；
High-definition picture is initialized, initialization fuzzy core is 0, according to super-resolution reconstruction universal model, for amplification
Multiple is S=p/q super-resolution reconstruction model, and wherein p and q are two relatively prime positive integers, degradation model are carried out discrete
The expression of change, is obtained：
Wherein, k represents kth frame image,Represent the value of the i-th row j column elements in the matrix that this discretization represents, DPUnder expression
Sampling matrix, FkFuzzy core is represented, R represents high-definition picture；Obtain a matrix Represent the discrete component of sequence of low resolution pictures" Valid " convolution with a size for E × E wave filters, E's
Span is [3,15]；If fuzzy core FkFuzzy core size is H × H, and H span is [3,15], by high resolution graphics
As R, fuzzy core FkWith down-sampling matrix DpCarry out representing matrix ξ；
ξ=SpΩf
WhereinWherein SpRepresent with
The related coefficient of multiplication factor, is determined according to multiplication factor；Multiplication factor is S=p/q, and p, q are two relatively prime integers,Represent R and the wave filter convolution that size is pE-p+H-1, CpE-p+1{F1Represent F1With the filter that size is pE-p+1
Ripple device convolution, the down-sampling matrix D in ΩpSize be (pE-p+1)2×E2；
Assert that f is full rank, therefore solve ξ=0, that is, ask for ξ kernel i.e. Ω=0；But by the big of matrix
Small to learn, the dimension of ξ kernel is to be greater than the dimension that Ω=0 solves：
Nullity (ξ) >=M=n (qE2)-(pE-p+H-1)2
Wherein nullity (ξ) represents the dimension in the spaces of ξ 0, and M represents the dimension that Ω=0 solves, and n represents picture number；
If μknWave filter of the size as E × E is represented, d represents row, and n represents row, ηdnIt is μdnRow vector decompose, size is
1 × E, then use ηdnTo represent that ξ kernel B is exactly：
UseRepresent μdnResult after multiple is p up-sampling,
Here final N matrix has been obtained；After obtaining matrix N, the regular terms to fuzzy core constraint can be obtainedΓ (R) is generally a high-pass filter；
If step 5. input picture is coloured image, then colour information regular terms is added in iterative equation, otherwise not
Addition；
Step 6., which replaces, estimates picture rich in detail image R and fuzzy core F, after the completion of iteration, exports high-definition picture；
Iterative equation is：
WhereinΓ (R) is a high-pass filter；DkRepresent kth
The down-sampling matrix of two field picture, FkThe fuzzy core of kth frame image is represented, λ, ω, φ represent regularization coefficient, and J (R) is to protecting
The regular terms of true item constraint, Q (F) represent the regular terms to fuzzy core constraint, and W (R) represents the regular terms to colour information constraint,
HkRepresent the registering matrix of kth frame image, LkActual low-resolution sequence is represented, the image obtained for step 1 or step 3,
Represent p rank norms；
If the low resolution of input is classified as gray-scale map, then regularization coefficientIf the low resolution of input
Sequence is coloured image, then
According to result above, in above formula, only F and R is unknown quantity, then F and R alternately can be asked
Solution, i.e., an initial value R is first substituted into, F can be solved, substitute into F after completing solves to R, and the above is repeated
Step, until reaching stopping criterion for iteration.
Further, S=p/q in step 2, wherein p and q are two relatively prime positive integers, then to former low resolution figure
As carrying out the secondary down-sampling that multiple is q.
Further, in the step 6, the colour information regular terms of addition isIts
InGradient operation, f are asked in representativer,fg,fbThe respectively R of high-resolution picture rich in detail, G, tri- components of B, x, y represent to represent
The position of ranks pixel.
The present invention realizes rational according to the theory analysis that original low-resolution image sequence is carried out to secondary down-sampling
The multiplication factor of rank, compensate for existing algorithm can only realize the deficiency of integer level multiplication factor.Meanwhile illustrate existing oversubscription
Resolution restructing algorithm proposes to add one in alternating minimization super-resolution reconstruction algorithm to the limitation of Color Image Processing
Regular terms comprising colour information, realize the optimization processing to coloured image.
Brief description of the drawings
Fig. 1 is the alternating minimization super-resolution reconstruction algorithm overall flow figure based on regularization.
Fig. 2, Fig. 3 and Fig. 4 are gray level image super-resolution schematic diagrames, and wherein Fig. 1 is artwork, and Fig. 2 is 2 times of multiplication factors
As a result, Fig. 3 is the result of 1.5 times of multiplication factors.
Fig. 5, Fig. 6, Fig. 7 and Fig. 8 are coloured image and actual super-resolution schematic diagram, and wherein Fig. 5 and Fig. 6 are artworks, Fig. 7
It is the result of 2 times of multiplication factors with Fig. 8.
Embodiment
A kind of alternating minimization high-definition picture reconstructing method based on regularization, this method include：
Step 1：Sequence of low resolution pictures is inputted, determines multiplication factor S, S2Less than or equal to the amount of images of input；
Step 2：If S is integer, step 4 is directly carried out；Otherwise, according to multiplication factor S, to former low-resolution image sequence
Row carry out secondary down-sampling, obtain down-sampled images；S=p/q, wherein p and q are two relatively prime positive integers, then to former low
Image in different resolution carries out the secondary down-sampling that multiple is q.
Step 3：The down-sampled images that step 2 is obtained carry out the image registration based on mutual information；Wherein mutual information calculates
Represent that other frames and the first frame do mutual information calculating in addition to the first two field picture；
Provided with reference picture f1(x, y) and image f to be matched2(x1,y1), f1The comentropy of (x, y) is H (f1), f2(x1,
y1) comentropy be H (f2), their combination entropy is H (f1,f2), then the mutual information between themCalculation formula is：
Step 4. initializes high-definition picture and fuzzy core, and constructs a matrix fuzzy core coefficient matrix N；
High-definition picture is initialized, initialization fuzzy core is 0, according to super-resolution reconstruction universal model, for amplification
Multiple is S=p/q super-resolution reconstruction model, and wherein p and q are two relatively prime positive integers, degradation model are carried out discrete
The expression of change, is obtained：
Wherein, k represents kth frame image,Represent the value of the i-th row j column elements in the matrix that this discretization represents, DPUnder expression
Sampling matrix, FkFuzzy core is represented, R represents high-definition picture；Obtain a matrix Represent the discrete component of sequence of low resolution pictures" Valid " convolution with a size for E × E wave filters, E's
Span is [3,15]；If fuzzy core FkFuzzy core size is H × H, and H span is [3,15], by high resolution graphics
As R, fuzzy core FkWith down-sampling matrix DpCarry out representing matrix ξ；
ξ=SpΩf
WhereinWherein SpRepresent with
The related coefficient of multiplication factor, is determined according to multiplication factor；Multiplication factor is S=p/q, and p, q are two relatively prime integers,Represent R and the wave filter convolution that size is pE-p+H-1, CpE-p+1{F1Represent F1With the filter that size is pE-p+1
Ripple device convolution, the down-sampling matrix D in ΩpSize be (pE-p+1)2×E2；
Assert that f is full rank, therefore solve ξ=0, that is, ask for ξ kernel i.e. Ω=0；But by the big of matrix
Small to learn, the dimension of ξ kernel is to be greater than the dimension that Ω=0 solves：
Nullity (ξ) >=M=n (qE2)-(pE-p+H-1)2
Wherein nullity (ξ) represents the dimension in the spaces of ξ 0, and M represents the dimension that Ω=0 solves, and n represents picture number；
If μknWave filter of the size as E × E is represented, d represents row, and n represents row, ηdnIt is μdnRow vector decompose, size is
1 × E, then use ηdnTo represent that ξ kernel B is exactly：
UseRepresent μdnResult after multiple is p up-sampling,
Here final N matrix has been obtained；After obtaining matrix N, the regular terms to fuzzy core constraint can be obtainedΓ (R) is generally a high-pass filter；
If step 5. input picture is coloured image, then colour information regular terms is added in iterative equation, otherwise not
Addition；
Step 6., which replaces, estimates picture rich in detail image R and fuzzy core F, after the completion of iteration, exports high-definition picture；
Iterative equation is：
WhereinΓ (R) is a high-pass filter；DkRepresent kth
The down-sampling matrix of two field picture, FkThe fuzzy core of kth frame image is represented, λ, ω, φ represent regularization coefficient, and J (R) is to protecting
The regular terms of true item constraint, Q (F) represent the regular terms to fuzzy core constraint, and W (R) represents the regular terms to colour information constraint,
HkRepresent the registering matrix of kth frame image, LkActual low-resolution sequence is represented, the image obtained for step 1 or step 3,
Represent p rank norms；
If the low resolution of input is classified as gray-scale map, then regularization coefficientIf the low resolution of input
Sequence is coloured image, then
The colour information regular terms of addition isWhereinLadder is asked in representative
Degree operation, fr,fg,fbThe respectively R of high-resolution picture rich in detail, G, tri- components of B, x, y represent to represent ranks pixel
Position；
According to result above, in above formula, only F and R is unknown quantity, then F and R alternately can be asked
Solution, i.e., an initial value R is first substituted into, F can be solved, substitute into F after completing solves to R, and the above is repeated
Step, until reaching stopping criterion for iteration.
Claims (3)
1. a kind of alternating minimization high-definition picture reconstructing method based on regularization, this method include：
Step 1：Sequence of low resolution pictures is inputted, determines multiplication factor S, S2Less than or equal to the amount of images of input；
Step 2：If S is integer, step 4 is directly carried out；Otherwise, according to multiplication factor S, former sequence of low resolution pictures is entered
The secondary down-sampling of row, obtains down-sampled images；
Step 3：The down-sampled images that step 2 is obtained carry out the image registration based on mutual information；Wherein mutual information, which calculates, represents
Other frames and the first frame do mutual information calculating in addition to the first two field picture；
Provided with reference picture f1(x, y) and image f to be matched2(x1,y1), f1The comentropy of (x, y) is H (f1), f2(x1,y1)
Comentropy is H (f2), their combination entropy is H (f1,f2), then the mutual information between themCalculation formula is：
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Step 4. initializes high-definition picture and fuzzy core, and constructs a matrix fuzzy core coefficient matrix N；
High-definition picture is initialized, initialization fuzzy core is 0, according to super-resolution reconstruction universal model, for multiplication factor
For S=p/q super-resolution reconstruction model, wherein p and q are two relatively prime positive integers, and degradation model is carried out into discretization
Represent, obtain：
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Wherein, k represents kth frame image,Represent the value of the i-th row j column elements in the matrix that this discretization represents, DPRepresent down-sampling square
Battle array, FkFuzzy core is represented, R represents high-definition picture；Obtain a matrix Represent the discrete component of sequence of low resolution pictures" Valid " convolution with a size for E × E wave filters, E's
Span is [3,15]；If fuzzy core FkFuzzy core size is H × H, and H span is [3,15], by high resolution graphics
As R, fuzzy core FkWith down-sampling matrix DpCarry out representing matrix ξ；
ξ=SpΩf
Wherein Wherein SpExpression and times magnification
The related coefficient of number, is determined according to multiplication factor；Multiplication factor is S=p/q, and p, q are two relatively prime integers,
Represent R and the wave filter convolution that size is pE-p+H-1, CpE-p+1{F1Represent F1With the wave filter convolution that size is pE-p+1, Ω
In down-sampling matrix DpSize be (pE-p+1)2×E2；
Assert that f is full rank, therefore solve ξ=0, that is, ask for ξ kernel i.e. Ω=0；But obtained by the size of matrix
Know, the dimension of ξ kernel is to be greater than the dimension that Ω=0 solves：
Nullity (ξ) >=M=n (qE2)-(pE-p+H-1)2
Wherein nullity (ξ) represents the dimension in the spaces of ξ 0, and M represents the dimension that Ω=0 solves, and n represents picture number；
If μknWave filter of the size as E × E is represented, d represents row, and n represents row, ηdnIt is μdnRow vector decompose, size be 1 ×
E, then use ηdnTo represent that ξ kernel B is exactly：
UseRepresent μdnResult after multiple is p up-sampling,
Here final N matrix has been obtained；After obtaining matrix N, the regular terms to fuzzy core constraint can be obtained
Γ (R) is generally a high-pass filter；
If step 5. input picture is coloured image, then colour information regular terms is added in iterative equation, is not otherwise added；
Step 6., which replaces, estimates picture rich in detail image R and fuzzy core F, after the completion of iteration, exports high-definition picture；
Iterative equation is：
WhereinΓ (R) is a high-pass filter；DkRepresent kth frame figure
The down-sampling matrix of picture, FkThe fuzzy core of kth frame image is represented, λ, ω, φ represent regularization coefficient, and J (R) is to fidelity item
The regular terms of constraint, Q (F) represent the regular terms to fuzzy core constraint, and W (R) represents the regular terms to colour information constraint, HkTable
Show the registering matrix of kth frame image, LkActual low-resolution sequence is represented, the image obtained for step 1 or step 3,Represent
P rank norms；
If the low resolution of input is classified as gray-scale map, then regularization coefficientIf the low-resolution sequence of input
For coloured image, then
According to result above, in above formula, only F and R is unknown quantity, then F and R alternately can be solved, i.e.,
An initial value R is first substituted into, F can be solved, substitute into F after completing solves to R, and above step is repeated,
Until reaching stopping criterion for iteration.
2. a kind of alternating minimization high-definition picture reconstructing method based on regularization as claimed in claim 1, its feature
It is two relatively prime positive integers in the S=p/q in the step 2, wherein p and q, then multiple is carried out to former low-resolution image
For q secondary down-sampling.
3. a kind of alternating minimization high-definition picture reconstructing method based on regularization as claimed in claim 1, its feature
In the step 6, the colour information regular terms of addition isWhereinGeneration
Table asks for gradient operation, fr,fg,fbThe respectively R of high-resolution picture rich in detail, G, tri- components of B, x, y represent to represent ranks number
The position of pixel.
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