CN107610048A - A kind of image super-resolution method returned based on projection dictionary learning and neighbour - Google Patents

A kind of image super-resolution method returned based on projection dictionary learning and neighbour Download PDF

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CN107610048A
CN107610048A CN201710679613.6A CN201710679613A CN107610048A CN 107610048 A CN107610048 A CN 107610048A CN 201710679613 A CN201710679613 A CN 201710679613A CN 107610048 A CN107610048 A CN 107610048A
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msubsup
mrow
msub
resolution
neighbour
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黄倩
张迪
叶枫
徐淑芳
王琪
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Hohai University HHU
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Abstract

The invention discloses a kind of image super-resolution method returned based on projection dictionary learning and neighbour.The present invention obtains synthesis and analytic type dictionary using projection dictionary learning method, and synthesis type dictionary base tissue neighbour is gathered, realizes the division finer to feature space.The optimal model based on 2 norms is solved, accelerates speed.When neighbour is organized, the local geometric characteristic of data is considered, more accurately recover the high-frequency information of high-definition picture, obtain higher-quality high-definition picture.

Description

A kind of image super-resolution method returned based on projection dictionary learning and neighbour
Technical field
It is more particularly to a kind of based on projection dictionary learning the invention belongs to computer vision and technical field of image processing The image super-resolution method returned with neighbour.
Background technology
Image Super-resolution belongs to computer vision and image processing field, is a classical image processing problem, has Important science and industrial research value.The target of Image Super-resolution is exactly, by given low-resolution image, to reconstruct its phase The high-definition picture answered so that in the case where reconstructed error is as small as possible, visual effect is good as far as possible.Main flow at present Image super-resolution method can be divided into three major types：Method based on interpolation；Method based on reconstruct；Method based on study.
Method based on interpolation, is a kind of basic ultra-resolution method, and its processing procedure would generally use local covariance Coefficient, fixing function core or adaptive structure core, are widely used because of the characteristics of its is simple and quick.But many situations Under, result caused by this kind of method can produce visual artifact with the increase of multiplication factor, such as：Sawtooth effect and fuzzy effect Should.Method based on reconstruct, it is assumed that low resolution image is obtained by high-definition picture by several degeneration factors, such as： Down-sampled and blurring.This kind of method emphasizes the importance of Reconstruction Constraints during super-resolution, thus, its obtained high-resolution Rate image often has excessively smooth and unnatural edge and ringing effect is produced near image border.Based on study Method, because using machine learning techniques from training focusing study to a large amount of prioris, thus obtain more preferable result. But this kind of method usually requires to solve and is based on l0Norm or l1The optimization problem of norm, its processing speed are very slow.
The content of the invention
In order to solve the technical problem that above-mentioned background technology proposes, the present invention is intended to provide a kind of based on projection dictionary learning The image super-resolution method returned with neighbour, the defects of overcoming prior art to exist, obtain higher-quality high-definition picture.
In order to realize above-mentioned technical purpose, the technical scheme is that：
A kind of image super-resolution method returned based on projection dictionary learning and neighbour, is comprised the following steps：
(1) concentrate to obtain full resolution pricture set from natural image common dataIts down-sampling is obtained corresponding Low-resolution image setWherein, subscript i represents the i-th width image in set；
(2) respectively fromWithHigh-resolution features set corresponding to middle extractionWith low resolution characteristic setClustered in low resolution feature space, closed for every a pair of cluster setsObtained using projection study dictionary To corresponding synthesis type dictionary DcWith analytic type dictionary Ωc, wherein, c=1,2,3 ..., C, C are the number of cluster centre；
(3) basisAnd Dc, calculate high-resolution neighbour setLow resolution neighbour gathersAnd the mapping matrix set of high-low resolution feature
(4) for each low resolution featureUsing DcAnd ΩcIt is rightClassified；
(5) basisClassification results, from corresponding DcIt is middle search withImmediate dictionary base, recycling are reflected accordingly Penetrate matrix FcReconstruct high-resolution features
(6) according to the high-resolution features set reconstructedRecover corresponding high-definition picture
Further, in step (2), by low-resolution imageUsing interpolation algorithm up-sample to corresponding high score Distinguish the equal sized of image；Then fromMiddle extraction high-definition picture set of blocksWith high-resolution features setAgain fromIn relevant position extract low-resolution image set of blocksWith low resolution characteristic set
In above formula, f1And f2For gradient high-pass filter horizontally and vertically, f3And f4For horizontal direction and hang down Nogata to Laplacian high-pass filter, " * " represent convolution algorithm.
Further, in step (6), by the high-resolution features set of reconstructPlus low-resolution image block collection CloseHigh-definition picture set of blocks corresponding to obtainingWillIn all fragments compositings into a high score rate Image
Further, in step (2), the optimization problem of projection dictionary learning is established：
In above formula, | | | |FExpression takes norm,λ is constant, dc,kFor Synthesis type dictionary DcK-th of dictionary base；
By the above-mentioned optimization problem of solution by iterative method, synthesis type dictionary D is obtainedcWith analytic type dictionary Ωc。
Further, in step (3), for synthesis type dictionary DcK-th of dictionary base dc,k,In look for max near Neighbour, compositionAgain fromIn look for max neighbours, formFor low resolution neighbourKth column vector, For high-resolution neighbourKth column vector；Then the mapping matrix F of high-low resolution feature is calculated according to following formulacKth Column vector
In above formula,ForTransposition, λ1For constant, I is unit matrix.
Further, in step (4), using following formula to a low resolution featureClassified：
In above formula, | | | |2Expression takes 2 norms, and my the optimal solution c obtained isAffiliated classification number.
Further, in step (5), in low resolution featureSynthesis type dictionary D corresponding to affiliated classification ccIn Search withImmediate dictionary base, according to mapping matrix F corresponding to the dictionary basecColumn vectorReconstruct corresponding high score Resolution feature
The beneficial effect brought using above-mentioned technical proposal：
The present invention obtains synthesis and analytic type dictionary using projection dictionary learning method, to synthesis type dictionary base tissue neighbour Set, realizes the division finer to feature space.The optimal model based on 2 norms is solved, accelerates speed.In tissue neighbour When, consider the local geometric characteristic of data, more accurately recover the high-frequency information of high-definition picture, obtain higher quality High-definition picture.
Brief description of the drawings
Fig. 1 is the overall flow figure of the present invention.
Embodiment
Below with reference to accompanying drawing, technical scheme is described in detail.
A kind of image super-resolution method returned based on projection dictionary learning and neighbour, as shown in figure 1, specific steps are such as Under.
Step 1：Full resolution pricture set is obtained from natural image common data sets (such as Image Net data sets)Its down-sampling is obtained into corresponding low-resolution image setWherein, subscript i represents the i-th width image in set.
Step 2：Respectively fromWithHigh-resolution features set corresponding to middle extractionWith low resolution feature set CloseClustered in low resolution feature space, closed for every a pair of cluster setsDictionary is learnt using projection Synthesis type dictionary D corresponding to obtainingcWith analytic type dictionary Ωc, wherein, c=1,2,3 ..., C, C are the number of cluster centre.
By low-resolution imageUp-sampled using interpolation algorithm to equal sized with corresponding full resolution pricture；Then FromMiddle extraction high-definition picture set of blocksWith high-resolution features setAgain fromIn relevant position Extract low-resolution image set of blocksWith low resolution characteristic set
In above formula, f1And f2For gradient high-pass filter horizontally and vertically, f3And f4For horizontal direction and hang down Nogata to Laplacian high-pass filter, " * " represent convolution algorithm.
Establish the optimization problem of projection dictionary learning：
In above formula, | | | |FExpression takes norm,λ is constant, dc,kFor Synthesis type dictionary DcK-th of dictionary base.
By the above-mentioned optimization problem of solution by iterative method, synthesis type dictionary D is obtainedcWith analytic type dictionary Ωc.Introduced for this Intermediate variable Ac, by above-mentioned optimization problem, relaxation is：
In above formula, τ is constant.It is divided into two parts during iterative.
1st, fixed Dc、Ωc, update Ac：
2nd, fixed Ac, update Dc、Ωc：
Iteration 1,2, solves Dc、Ωc。
Step 3：According toAnd Dc, calculate high-resolution neighbour setLow resolution neighbour gathersAnd the mapping matrix set of high-low resolution feature
For synthesis type dictionary DcK-th of dictionary base dc,k,In look for max neighbours, formAgain fromIn look for Max neighbours, compositionFor low resolution neighbourKth column vector,For high-resolution neighbourKth Column vector.
In order to obtain the coefficient x required for reconstruct high-resolution features, following optimization objective function is first solved：
There are analytic solutions in the problem, concrete form is：
So corresponding high-resolution features can be tried to achieve by following formula：
The major part of above-mentioned formula is and inputIt is unrelated, thus can be come out with off-line calculation, as mapping matrix：
Wherein,ForTransposition, λ1For constant, I is unit matrix.
Step 4：For each low resolution featureUsing DcAnd ΩcIt is rightClassified.
Using following formula to a low resolution featureClassified：
In above formula, | | | |2Expression takes 2 norms, and my the optimal solution c obtained isAffiliated classification number.
Step 5：According toClassification results, from corresponding DcIt is middle search withImmediate dictionary base, recycle corresponding Mapping matrix FcReconstruct high-resolution features
In low resolution featureSynthesis type dictionary D corresponding to affiliated classification ccIt is middle search withImmediate dictionary Base, according to mapping matrix corresponding to the dictionary baseReconstruct corresponding high-resolution features
Step 6：According to the high-resolution features set reconstructedRecover corresponding high-definition picture
By the high-resolution features set of reconstructPlus low-resolution image set of blocksObtain corresponding high score Resolution image block setWillIn all fragments compositings into a high score rate image
The technological thought of embodiment only to illustrate the invention, it is impossible to protection scope of the present invention is limited with this, it is every according to Technological thought proposed by the present invention, any change done on the basis of technical scheme, each falls within the scope of the present invention.

Claims (7)

  1. A kind of 1. image super-resolution method returned based on projection dictionary learning and neighbour, it is characterised in that：Comprise the following steps：
    (1) concentrate to obtain full resolution pricture set from natural image common dataIts down-sampling is obtained into corresponding low resolution Rate image collectionWherein, subscript i represents the i-th width image in set；
    (2) respectively fromWithHigh-resolution features set corresponding to middle extractionWith low resolution characteristic set Clustered in low resolution feature space, closed for every a pair of cluster setsObtained correspondingly using projection study dictionary Synthesis type dictionary DcWith analytic type dictionary Ωc, wherein, c=1,2,3 ..., C, C are the number of cluster centre；
    (3) basisAnd Dc, calculate high-resolution neighbour setLow resolution neighbour gathersAnd Mapping matrix set { the F of high-low resolution featurec}；
    (4) for each low resolution featureUsing DcAnd ΩcIt is rightClassified；
    (5) basisClassification results, from corresponding DcIt is middle search withImmediate dictionary base, recycle corresponding mapping square Battle array FcReconstruct high-resolution features
    (6) according to the high-resolution features set reconstructedRecover corresponding high-definition picture
  2. 2. the image super-resolution method returned according to claim 1 based on projection dictionary learning and neighbour, it is characterised in that： In step (2), by low-resolution imageUp-sampled using interpolation algorithm to equal sized with corresponding full resolution pricture； Then fromMiddle extraction high-definition picture set of blocksWith high-resolution features setAgain fromIn it is corresponding Position extracts low-resolution image set of blocksWith low resolution characteristic set
    <mrow> <msubsup> <mi>p</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>=</mo> <msubsup> <mi>p</mi> <mi>H</mi> <mi>i</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>H</mi> <mi>i</mi> </msubsup> </mrow>
    <mrow> <msubsup> <mi>y</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>*</mo> <msubsup> <mi>p</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>;</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>*</mo> <msubsup> <mi>p</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>;</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> <mo>*</mo> <msubsup> <mi>p</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>;</mo> <msub> <mi>f</mi> <mn>4</mn> </msub> <mo>*</mo> <msubsup> <mi>p</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>&amp;rsqb;</mo> </mrow>
    In above formula, f1And f2For gradient high-pass filter horizontally and vertically, f3And f4For horizontal direction and Vertical Square To Laplacian high-pass filter, " * " represent convolution algorithm.
  3. 3. the image super-resolution method returned according to claim 2 based on projection dictionary learning and neighbour, it is characterised in that： In step (6), by the high-resolution features set of reconstructPlus low-resolution image set of blocksCorresponding to obtaining High-definition picture set of blocksWillIn all fragments compositings into a high score rate image
  4. 4. the image super-resolution method returned according to claim 1 based on projection dictionary learning and neighbour, it is characterised in that： In step (2), the optimization problem of projection dictionary learning is established：
    <mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <msub> <mi>D</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;Omega;</mi> <mi>i</mi> </msub> </mrow> </munder> <munderover> <mo>&amp;Sigma;</mo> <mi>c</mi> <mi>C</mi> </munderover> <mo>|</mo> <mo>|</mo> <msubsup> <mi>Y</mi> <mi>L</mi> <mi>c</mi> </msubsup> <mo>-</mo> <msub> <mi>D</mi> <mi>c</mi> </msub> <msub> <mi>&amp;Omega;</mi> <mi>c</mi> </msub> <msubsup> <mi>Y</mi> <mi>L</mi> <mi>c</mi> </msubsup> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&amp;lambda;</mi> <mo>|</mo> <mo>|</mo> <msub> <mi>&amp;Omega;</mi> <mi>c</mi> </msub> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>L</mi> <mi>c</mi> </msubsup> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> <mo>&amp;le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
    In above formula, | | | |FExpression takes norm,λ is constant, dc,kFor synthesis type Dictionary DcK-th of dictionary base；
    By the above-mentioned optimization problem of solution by iterative method, synthesis type dictionary D is obtainedcWith analytic type dictionary Ωc。
  5. 5. the image super-resolution method returned according to claim 4 based on projection dictionary learning and neighbour, it is characterised in that： In step (3), for synthesis type dictionary DcK-th of dictionary base dc,k,In look for max neighbours, formAgain from In look for max neighbours, form For low resolution neighbourKth column vector,For high-resolution neighbour's Kth column vector；Then the mapping matrix F of high-low resolution feature is calculated according to following formulacKth column vector
    <mrow> <msubsup> <mi>F</mi> <mi>k</mi> <mi>c</mi> </msubsup> <mo>=</mo> <msubsup> <mi>N</mi> <mrow> <mi>H</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msup> <msubsup> <mi>N</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mi>T</mi> </msup> <msubsup> <mi>N</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mi>I</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>N</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>c</mi> </msubsup> </mrow>
    In above formula,ForTransposition, λ1For constant, I is unit matrix.
  6. 6. the image super-resolution method returned according to claim 1 based on projection dictionary learning and neighbour, it is characterised in that： In step (4), using following formula to a low resolution featureClassified：
    <mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mo>|</mo> <mo>|</mo> <msubsup> <mi>y</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>-</mo> <msub> <mi>D</mi> <mi>c</mi> </msub> <msub> <mi>&amp;Omega;</mi> <mi>c</mi> </msub> <msubsup> <mi>y</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow>
    In above formula, | | | |2Expression takes 2 norms, and my the optimal solution c obtained isAffiliated classification number.
  7. 7. the image super-resolution method returned according to claim 1 based on projection dictionary learning and neighbour, it is characterised in that： In step (5), in low resolution featureSynthesis type dictionary D corresponding to affiliated classification ccIt is middle search withImmediate word Allusion quotation base, according to mapping matrix F corresponding to the dictionary basecColumn vectorReconstruct corresponding high-resolution features
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CN104899830A (en) * 2015-05-29 2015-09-09 清华大学深圳研究生院 Image super-resolution method
CN105787899A (en) * 2016-03-03 2016-07-20 河海大学 Rapid image super-resolution method based on self-adaptive regression

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CN104899830A (en) * 2015-05-29 2015-09-09 清华大学深圳研究生院 Image super-resolution method
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Publication number Priority date Publication date Assignee Title
CN113628108A (en) * 2021-07-05 2021-11-09 上海交通大学 Image super-resolution method and system based on discrete representation learning and terminal
CN113628108B (en) * 2021-07-05 2023-10-27 上海交通大学 Image super-resolution method and system based on discrete representation learning and terminal

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Application publication date: 20180119