CN107085834A - A kind of image de-noising method based on image rotation and piecemeal singular value decomposition - Google Patents
A kind of image de-noising method based on image rotation and piecemeal singular value decomposition Download PDFInfo
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Abstract
The invention discloses a kind of image de-noising method based on image rotation and piecemeal singular value decomposition, piecemeal rotation is carried out to original input picture first；Secondly the postrotational image block of search, and similitude matching is carried out according to image block；Finally decomposed to carrying out the different value of two peacekeeping one dimension odds inside and outside the similar block that the match is successful respectively, matrix projection coefficient is shunk using soft, hard compromise method threshold value, 1D SVD inverse transformations and 2D SVD inverse transformations are carried out to the projection coefficient after contraction, final image denoising is realized.This method first carries out piecemeal rotation before denoising to image, eliminates image information decay in block, shortens processing time, carries out the singular value decomposition of different dimensions respectively inside and outside image, and improve noiseproof feature on the basis of traditional svd algorithm.
Description
Technical field
The invention belongs to image processing field, and in particular to a kind of image based on image rotation and piecemeal singular value decomposition
Denoising method.
Background technology
With the popularization of all kinds of digital implementations and digital product, Digital Image Processing has become digital technology and computer
One study hotspot of technology crossing domain.Digital Image Processing, refers to visualize using in computer science research and production
The digital processing of information.By the processing to image information to meet the visual psychology of people or the behavior of application demand.We are big
Many residing environment is under complex state, our life can be influenceed down to extraneous factor, during original image is gathered,
There are unkownable factors can damage the image of collection, it is seen that or invisible noise can also cause to do to varying degrees to image
Disturb, cause image quality decrease.But how to carry out effective, accurate denoising to image turns into important research problem of today.
By development in recent years, image denoising also emerges numerous research methods, singular value decomposition as it is a kind of very
Important non-linear filtering method, one-dimensional singular value decomposition has good precision and high efficiency, but it can not fully be removed
Correlation in image, is caused after redundancy in block, image vector, adds the complexity of calculating；Two-dimentional singular value decomposition is gone
Redundancy in block can be improved by making an uproar, and reduced useful information and be lost in, retain the more practical informations of image, lift the accurate of image denoising
Property, while being also improved in amount of calculation, the information of original image, enhancing vision effect can be preferably retained while denoising
Really.But the principal direction of this method is not complete, imperfect comprising image information, cause denoising accuracy not high.
The content of the invention
It is an object of the invention to provide a kind of image de-noising method based on image rotation and piecemeal singular value decomposition, solve
The problem of existing denoising method image information is imperfect, denoising accuracy is not high.
The technical solution adopted by the present invention is, a kind of image denoising side based on image rotation and piecemeal singular value decomposition
Method, comprises the following steps：
Step 1：Piecemeal processing first is carried out to original input picture, non-overlapped rectangular block is divided into；Then using linear
The method of fitting determines the anglec of rotation θ of image block, then by each image block rotation-θ degree of original image, obtains horizontal direction
Image；
Step 2：The postrotational image block of piecemeal is searched for, and is matched according to the similitude of image block, every group is obtained
With successful similar block；
Step 3：Every group of similar block that the match is successful is carried out to carry out 2D SVD inside singular value decomposition, similar block, it is similar
1D SVD are used between block block；
Step 4：Matrix projection coefficient is shunk using threshold value shrinkage method, 1D is carried out to the projection coefficient after contraction
SVD inverse transformations and 2D SVD inverse transformations, complete image denoising.
The features of the present invention is also resided in：
Further, step 1：The anglec of rotation θ of image block is determined using the method for linear fit, is comprised the following steps：
A. setting curve f (x) is with straight line y squared difference and is object function J, and formula is as follows：
Define following matrix form
Wherein, A is the corresponding coefficient column matrix of straight line y=ax+b, and Y is the row square corresponding to straight line y each value
Battle array.
The corresponding matrix forms of object function J are in formula (1)
J=(ATXT-YT)XA-(ATXT-YT)Y (3)
B. the principle of least square method is that curve f (x) and straight line y difference are summed, and makes square i.e. target of its sum
Function J takes minimum value, object function is reached minimum value, then formula (3) need to seek partial derivative to matrix A, make partial derivative be equal to
Zero obtains matrix A.
Abbreviation formula (4), can obtain matrix A=X-1(XX-1)TY, each value x substituted into straight line y=ax+bi
And yi, obtain straight line y coefficient a and b.
The linear equation obtained more than, it can be deduced that the anglec of rotation θ of image：
Further, step 2：Matching is carried out according to the similitude of image block and uses K- means clustering algorithms, it thinks substantially
Want M data object being divided into K cluster, choose corresponding cluster centre so that data in K cluster of division and
The distance between this cluster centre point difference is minimum, for ease of calculating, and directly obtains in each cluster data to this cluster centre point
The square value of range difference, between the two apart from small, i.e., square value is also similarly, to obtain the difference of two squares, and being chosen whether according to condition will
The determination of new cluster centre is carried out, above-mentioned steps are repeated, until finding out the point and former and later two cluster centres in space
The difference of two squares, untill meeting decision condition, it is determined that new cluster centre.This method comprises the following steps：
(1) by A1And AΩIt is set as the initial cluster center of K- means Methods, and obtains each data object to poly-
The distance between class center；For the ease of calculating, what is obtained is square distance and root of each data object to cluster centre
Each data object is divided according to following formula result of calculation.
Wherein：SjRepresent the point in space, OkRepresent each cluster centre, ΩjAnd ΩkS is represented respectivelyjAnd OkIt is corresponding to make an uproar
Sound.
(2) in each class, according to order, a data object is selected as new cluster centre, and calculate space
Point S and two cluster centres square distance and its difference (difference represents consumption consume).
Consume=Dk(S,Oi')-Dk(S,Oi)+2σ2 (8)
Corresponding, Dk(S,Oi') in S ∈ Ci', Dk(S,Oi) in S ∈ Ci, wherein Ci' represent the class that newly divides and
C, Oi' represent the central point of original class sum, σ2Represent noise variance.
According to following judgment criteria, judging image block, whether the match is successful；
If consume<0, then by original cluster centre OiReplace with new cluster centre Oi', return in repeat step (2)
Consume calculating is consumed, until the consumption calculated meets consume>0；Conversely, cluster centre is no longer converted, then it represents that
The match is successful for image block.
K- means Methods have stronger stability, small by noise jamming, while calculating can also be reduced largely
Error, on the premise of it more can retain image information, there is a good denoising performance, optimize image visual effect.
Further, the threshold value shrinkage method used in step 4 is soft, hard compromise method threshold value shrinkage method, using equation below：
Wherein, 0 ＜ λ ＜ 1.
The separation of image and noise is realized using threshold value shrinkage method that is soft, compromising firmly, conventional threshold values shrinkage method is improved
Discontinuity, embody threshold value shrink after continuity, be mathematically easily processed, more smooth, vision can be obtained
On be easy to receive image.
Further, in formula (14), T=2.7 σ.
The beneficial effects of the invention are as follows compared with the existing methods, the inventive method is at two-dimentional singular value decomposition denoising
Image rotation is added in reason, because the different directions of image have the main information of its directionality, it is necessary to convert images into vertical
Or horizontal direction, it can so reduce the unnecessary loss of image information；In the threshold value shrink process to matrix projection coefficient, adopt
With the combination of soft-threshold shrinkage method and hard -threshold shrinkage method, soft, hard -threshold compromise method makes up hard -threshold shrinkage method data not
Continuity, improves the constant error of soft-threshold shrinkage method, improves the accuracy of coefficients model, preferably retains image letter
Breath, meets the requirement of real-time of image procossing.
Brief description of the drawings
Fig. 1 is the schematic diagram of image de-noising method of the present invention；
Fig. 2 is the flow chart of similar block matching algorithm.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and detailed description, but the present invention is not limited to
These embodiments.
The image de-noising method principle of the present invention according to following steps as shown in figure 1, specifically implement：
Step 1：Piecemeal rotation is carried out to original input picture；
(1) piecemeal processing is first carried out to image, sets grandfather tape noise image size as I1×I2, by grandfather tape noise pattern
As being divided into non-overlapped square block, each square block size completed that divides is that (it is m × n that can also be divided into size to m × m
Rectangular blocks).Because the master image information included in each image block is different, so needing to enter the image block after division
Row piecemeal rotates, the problem of determination of the anglec of rotation is often very crucial during image rotation.
(2) angle of inclination of image block is determined using the method for linear fit, basic thought is that first setting one is smooth
Curve y=f (x), is fitted using straight line y=ax+b and curve f (x), obtains anglec of rotation θ, specific method application is minimum
Square law, obtains curve f (x) and straight line y residual epsiloni=f (xi)-yi, its quadratic sum is reached into minimum.Rotation is to determine below
The detailed process of angle.
A. setting curve f (x) is with straight line y squared difference and is object function J, and formula is as follows：
Define following matrix form
Wherein, A is the corresponding coefficient column matrix of straight line y=ax+b, and Y is the row square corresponding to straight line y each value
Battle array.
The corresponding matrix forms of object function J are in formula (1)
J=(ATXT-YT)XA-(ATXT-YT)Y (3)
B. the principle of least square method is that curve f (x) and straight line y difference are summed, and makes square i.e. target of its sum
Function J takes minimum value, object function is reached minimum value, then formula (3) need to seek partial derivative to matrix A, make partial derivative be equal to
Zero obtains matrix A.
Abbreviation formula (4), can obtain matrix A=X-1(XX-1)TY, each value x substituted into straight line y=ax+bi
And yi, obtain straight line y coefficient a and b.
The linear equation obtained more than, it can be deduced that the anglec of rotation θ of image：
The anglec of rotation θ of image block is obtained from above, by each image block rotation-θ degree of original image, horizontal direction is obtained
Image.
Step 2：The postrotational image block of piecemeal is searched for, and is matched according to the similitude of image block, as indicated with 2, tool
Body is implemented as follows：
Original image is carried out after non-overlapped division, each square of block size is m × m (images divided in step 1
Block), use AΩThis square of block essential characteristic is represented, the benchmark of similar Block- matching is to utilize noisy image block AΩAfter the completion of division
Other noisy image (A1, A2...) block progress similitude contrast, the two matching is combined.Detailed process is as follows：
(1) by A1And AΩIt is set as the initial cluster center of K- means Methods, and obtains each data object to poly-
The distance between class center；For the ease of calculating, what is obtained is square distance and root of each data object to cluster centre
Each data object is divided according to following formula result of calculation.
Wherein：SjRepresent the point in space, OkRepresent each cluster centre, ΩjAnd ΩkS is represented respectivelyjAnd OkIt is corresponding to make an uproar
Sound.
(2) in each class, according to order, a data object is selected as new cluster centre, and calculate space
Point S and two cluster centres square distance and its difference (difference represents consumption consume).
Consume=Dk(S,Oi')-Dk(S,Oi)+2σ2 (8)
Corresponding, Dk(S,Oi') in S ∈ Ci', Dk(S,Oi) in S ∈ Ci, wherein Ci' represent the class that newly divides and
C, Oi' represent the central point of original class sum, σ2Represent noise variance.
According to following judgment criteria, judging image block, whether the match is successful；
If consume<0, then by original cluster centre OiReplace with new cluster centre Oi', return in repeat step (2)
Consume calculating is consumed, until the consumption calculated meets consume>0；Conversely, cluster centre is no longer converted, then it represents that
The match is successful for image block.
Step 3：The similar image block that the match is successful is carried out carrying out 2DSVD, similar block inside singular value decomposition, similar block
1D SVD are used between block, detailed process is as follows：
(1) 2D SVD are carried out inside similar block
Every group of similar block image has been obtained by aforesaid operations, due to that can have redundancy inside similar block, so
Need first to carry out related removal with 2D SVD to the inside of similar block, finally remove redundancy among image blocks with 1D SVD again.
Give one group of similar image blockIt is considered thatIt is the image block A by not Noise0With noise ΩiConstitute,
Need to calculate the covariance matrix of the row and column of image block, willThe corresponding eigenmatrix of covariance matrix is projected to, is obtained
Projection coefficient matrix.
Row-row covariance matrix and Lie-row covariance matrix it is as follows：
U2dAnd V2dThe corresponding eigenmatrixes of respectively X and Y, willProject on eigenmatrix, obtain
Wherein, W0It is diagonal matrix, A0Project obtained projection coefficient matrix W0The full detail of noise-free picture block is included, it is right
Diagonal element carries out coefficient threshold contraction, can extractNoise-free picture information in image block.
(2) 1D SVD are carried out between similar block block
By 2-D dataThe conversion coefficient obtained after being projected with 2D SVDVectorization is carried out, is gone with 1D SVD
Except the redundancy between similar block, similarly 2D SVD processing procedures, calculate the eigenmatrix V of covariance matrix1 d, by WΩProject to
V1 dOn, obtain：
Handle, removed inside similar block with the correlation between block by above step, can be by making an uproar in image block
Sound is effectively removed.
Step 4：According to the result of above step, matrix projection coefficient is shunk using soft, hard compromise method threshold value, after contraction
Projection coefficient carry out 1D SVD inverse transformations and 2D SVD inverse transformations, and evaluate using Y-PSNR the denoising of this method and imitate
Really.
The present invention compromises method to shrink matrix projection coefficient using soft, hard -threshold, using equation below：
Wherein, λ value is between 0 to 1, as λ=0, to be equal to hard -threshold shrinkage method, as λ=1, is equal to soft
Threshold value shrinkage method.This method compensate for the deficiency of soft-threshold and hard -threshold shrinkage method, can reach preferable threshold value contractive effect.
Threshold value T is generally set to T=2.7 σ, 1D SVD inverse transformations are carried out to the projection coefficient after contraction and 2D SVD are inverse
Conversion, obtains the similar image block after denoising, and carrying out aforesaid operations to the similar image block after each component masses respectively (repeats
Step 4, remaining each group of similar block carry out block and block in inverse transformation), it is possible to the original noisy image that obtains go
Whole sub-picture after making an uproar.
Denoising Algorithm under the different noise intensities of table 1 compares (dB)
| Noise variance (σ) | Piecemeal SVD | Piecemeal rotates SVD | The inventive method |
| 5 | 34.3155 | 34.4154 | 34.4228 |
| 10 | 29.7024 | 29.9102 | 30.3245 |
| 15 | 27.8216 | 28.1308 | 28.9276 |
| 20 | 26.5132 | 26.9249 | 27.8059 |
| 25 | 25.9371 | 26.4165 | 27.5431 |
| 30 | 25.3223 | 25.9249 | 27.3214 |
Using Y-PSNR, SVD Denoising Algorithm is rotated with piecemeal by contrasting piecemeal SVD, it can be seen that the present invention
Method used is better than the traditional denoising method of both the above, in the case where noise variance is 25, Denoising Algorithm score of the present invention
Block svd algorithm improves 1.606dB, and 1.1266dB is improved than piecemeal rotation svd algorithm, and with the increasing of noise variance
Greatly, there is apparent advantage compared to other svd algorithms in the denoising effect of inventive algorithm.
Claims (5)
1. a kind of image de-noising method based on image rotation and piecemeal singular value decomposition, it is characterised in that comprise the following steps：
Step 1：Piecemeal processing first is carried out to original input picture, non-overlapped rectangular block is divided into；Then linear fit is used
Method determine the anglec of rotation θ of image block, then by each image block rotation-θ degree of original image, obtain the figure of horizontal direction
Picture；
Step 2：The postrotational image block of piecemeal is searched for, and is matched according to the similitude of image block, every group is obtained and matches into
The similar block of work(；
Step 3：Every group of similar block that the match is successful is carried out to carry out 2D SVD, similar block block inside singular value decomposition, similar block
Between use 1D SVD；
Step 4：Matrix projection coefficient is shunk using threshold value shrinkage method, it is inverse to carry out 1D SVD to the projection coefficient after contraction
Conversion and 2D SVD inverse transformations, complete image denoising.
2. the image de-noising method according to claim 1 based on image rotation and piecemeal singular value decomposition, its feature exists
In determining that the anglec of rotation θ of image block comprises the following steps using the method for linear fit described in step 1：
A. setting curve f (x) is with straight line y squared difference and is object function J, and formula is as follows：
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<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mi>n</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
The linear equation obtained more than, obtains the anglec of rotation θ of image：
3. the image de-noising method according to claim 1 based on image rotation and piecemeal singular value decomposition, its feature exists
In, described in step 2 according to the similitude of image block carry out matching use K- means clustering algorithms, comprise the following steps：
(1) A is usedΩThe essential characteristic of square block after dividing is represented, other noisy images are A1, A2...；By A1And AΩIt is set as
The initial cluster center of K- means Methods, and obtain each data object to cluster centre square distance and, under
Formula result of calculation is divided each data object；
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<mi>D</mi>
<mi>k</mi>
</msub>
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<mo>(</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>O</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>O</mi>
<mi>k</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&Omega;</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&Omega;</mi>
<mi>k</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
(2) in each class, according to order, select a data object as new cluster centre, and calculate spatial point S with
Square distance sum its difference consume of two cluster centres,
Consume=Dk(S,Oi')-Dk(S,Oi)+2σ2 (8)
According to following judgment criteria, judging image block, whether the match is successful；
If consume<0, then by original cluster centre OiReplace with new cluster centre Oi', return in repeat step (2) and consume
Consume calculating, until the consumption calculated meets consume>0；Conversely, cluster centre is no longer converted, then it represents that image
Block- matching success.
4. the image de-noising method according to claim 1 based on image rotation and piecemeal singular value decomposition, its feature exists
In threshold value shrinkage method described in step 4 is soft, hard compromise method threshold value shrinkage method, using equation below：
<mrow>
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<mi>W</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>,</mo>
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</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>sgn</mi>
<mo>&lsqb;</mo>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>,</mo>
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</mrow>
<mo>&rsqb;</mo>
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<mo>-</mo>
<mi>&lambda;</mi>
<mi>T</mi>
<mo>&rsqb;</mo>
</mrow>
</mtd>
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<mrow>
<mo>|</mo>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>&GreaterEqual;</mo>
<mi>T</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>|</mo>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo><</mo>
<mi>T</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, 0 ＜ λ ＜ 1.
5. the image de-noising method according to claim 4 based on image rotation and piecemeal singular value decomposition, its feature exists
In, in the formula (14), T=2.7 σ.
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