CN108198140A - Three-dimensional collaboration filtering and noise reduction method based on NCSR models - Google Patents
Three-dimensional collaboration filtering and noise reduction method based on NCSR models Download PDFInfo
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Abstract
The invention discloses the three-dimensionals based on NCSR models to cooperate with filtering and noise reduction method, the specific steps are：Using Canny operator extraction noisy image edge pixel points, the coordinate of the edge pixel point is stored in W, is achieved in the classification of pixel；Noisy image in step 1 is grouped by step 2 by way of Block- matching；Step 3 will respectively be grouped image block and carry out collaboration filtering and noise reduction in step 2；Step 4, the image weighting average after step 3 denoising are polymerize, and acquire the final estimated value of image；Subarea processing is carried out to noisy image, further improves the readability of image detail part；Three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models is filtered noise using the Filtering Formula in NCSR models, takes full advantage of the non local similitude of image, hence it is evident that reduce the halation and ringing effect in denoising result.
Description
Technical field
The invention belongs to technical field of image processing, and in particular to the three-dimensional collaboration filtering and noise reduction side based on NCSR models
Method.
Background technology
In recent years, pass through the properties study to picture noise and image own signal, many scholars and researcher
Constantly propose new denoising method.The common objective of these methods is all：It can retain while denoising is realized more
Image detail information.For a width natural image, all there is very big correlations for structural texture feature.Therefore, nothing
By be directly pixel value is averaging processing with spatial domain method or using frequency domain method by image converted again to transformation
Coefficient carries out threshold process, is all to take full advantage of image part in itself and non local correlative character preferably goes to obtain
It makes an uproar effect.
All it is only to make an uproar by comparing the gray value of single pixel to containing using the method that local similarity carries out denoising
The pixel of sound is handled, and the effect of anticipation is not achieved in the robustness of algorithm.For this defect of local denoising method, research
Persons try hard to excavate the non local correlation of image, further improve denoising effect.NL- is proposed first in Buades et al.
This non local denoising method of Means, this method provide new thinking for later many non local denoising methods.Wherein,
BM3D algorithms are the relatively good non local Denoising Algorithms of generally acknowledged denoising effect, when its algorithm can overcome NL-Means well
Between this excessively high defect of complexity.Image detail can more be protected and the non-of image is obtained within the relatively short time
Local similarity is simultaneously used.But occur halation, ring and mosaic effect in the denoising effect of BM3D.Since it is adopted
Formula is filtered with simple hard -threshold to carry out part and non local filtering to one group of image block, and the filtering formula is only applicable in
In the local filtration of image.Can usually image border be made ringing effect occur when being filtered to non local image block.
Invention content
It is an object of the present invention to provide the three-dimensional collaboration filtering and noise reduction method based on NCSR models, using different filtering modes
Fringe region and smooth domain to image are separately handled, and can improve the clarity of image after processing.
The technical solution adopted in the present invention is, the three-dimensional collaboration filtering and noise reduction method based on NCSR models, specifically according to
Following steps are implemented：
Step 1, using Canny operator extraction noisy image edge pixel points, the coordinate of the edge pixel point is stored in
In array W；
Noisy image in step 1 is grouped by step 2 by way of Block- matching, obtains multiple grouping image blocks；
Step 3 will respectively be grouped image block and carry out collaboration filtering and noise reduction in step 2；
Grouping image block solution after step 3 denoising is formed multiple images block by step 4, same for having in original image
Each image block of one coordinate is polymerize by average weighted mode, acquires the final estimated value of image.
Step 2 the specific steps are：The position of reference block is determined first, and from the image upper left corner, the image block of first 8 × 8 is opened
Begin as first reference block, the position of next reference block is three pixels of translation to the right or downwards, using each reference block in
39 × 39 region of the heart is the neighborhood where current reference block, all with referring to the identical image blocks of block size all in neighborhood
It is candidate blocks, traverses candidate blocks all in neighborhood and its Euclidean distance between current reference block is obtained, select 16 Europe
The minimum candidate blocks of formula distance form a grouping as one group of similar block, this group of similar block with corresponding reference block.
The method for solving of Euclidean distance is：
In formula (1), dnoisyRepresent Euclidean distance, | | | |2Represent l-2 normal forms, ZxRRepresent the pixel value of reference block, ZxGeneration
The pixel value of candidate block in table neighborhood,Represent the pixel number in an image block.
Step 3 the specific steps are：
Step 3.1, all image blocks are required for carrying out local two-dimensional wavelet transformation first, then by being referred in each grouping
Whether the position of the central pixel point of block in W carries out three-dimensional collaboration filtering and noise reduction to select step a or step b, and estimation is each
The sparse coefficient of image block；
If a. the position of current group internal reference block central pixel point is in W, formula (2) in NCSR models pair is used
This group of image block carries out third dimension collaboration filtering；
If b. the position of current group internal reference block central pixel point is not in W, the formula (3) in NCSR models is used
To carry out this group of image block third dimension collaboration filtering；
In formula (2), (3),Represent the estimated value to image block sparse coefficient, α represents the sparse coefficient of image block, β tables
Show the average coefficient value of one group of image block, l1=c1λ, l2=c2γ, c1And c2All it is constant；
Step 3.2, after carrying out collaboration filtering to the sparse coefficient value of image block by step 3.1, the image that is each grouped
Block all carries out 2-d wavelet inverse transformation and obtains the pixel value on its spatial domain.
The specific of the final estimated value of step 4 image asks the method to be：
Step 4.1, the weight for obtaining multiple estimated values at same position：
In formula (4), NxRFor the number for multiple estimated values that same position occurs, σnFor original image noise variance；
Step 4.2, acquired using formula (5) it is after image block polymerization after final denoising as a result,
In formula (5),For the pixel estimated value that an image block obtains after non local filtering, xRFor in image
A reference block, xmFor one group of image some similar block in the block,For xmThe square features function at place,For the estimated value after final image denoising.
The present invention has the beneficial effect that：
1) the present invention is based on the three-dimensional collaboration filtering and noise reduction methods of NCSR models to carry out subarea processing (i.e. to noisy image
It is divided into fringe region and smooth domain), further improve image detail part (such as：Texture, edge etc.) readability.
2) the present invention is based on the three-dimensional collaboration filtering and noise reduction methods of NCSR models to utilize the Filtering Formula pair in NCSR models
Noise is filtered, and takes full advantage of the non local similitude of image, hence it is evident that reduces the halation and ring effect in denoising result
It should.
Description of the drawings
Fig. 1 is the flow chart of the three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models；
Fig. 2 is the image for experiment the present invention is based on the three-dimensional collaboration filtering and noise reduction method of NCSR models；
Fig. 3 is Cameraman (256 × 256) images by the schematic diagram after different degrees of Gaussian noise pollution；
Fig. 4 is to carry out pixel using Canny operators in the three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models
The schematic diagram of classification；
Fig. 5 is Block- matching process schematic in the three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models；
Fig. 6 is the similar packet diagram of three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models；
Fig. 7 be use the present invention is based on the three-dimensional collaboration filtering and noise reduction method of NCSR models for Cameraman (256 ×
256) schematic diagram after image denoising；
Fig. 8 is identical the present invention is based on the three-dimensional collaboration filtering and noise reduction method denoising result of NCSR models with BM3D algorithms
The contrast effect figure of denoising result under noise intensity；
Fig. 9 is that the present invention is based on the three-dimensional collaboration filtering and noise reduction method of NCSR models and other outstanding Denoising Algorithms in recent years
Comparison diagram.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawings and detailed description.
The present invention is based on the three-dimensional collaboration filtering and noise reduction method of NCSR models, as shown in Figure 1, specifically according to following steps reality
It applies：
Step 1, using Canny operator extraction noisy image edge pixel points, the coordinate of the edge pixel point is stored in
In array W；
The classification of pixel is divided into two classes, and one kind is the pixel of smooth domain, and one kind is the pixel of fringe region；
Noisy image in step 1 is grouped by step 2 by way of Block- matching, obtains multiple grouping image blocks；
Step 2 the specific steps are：The position of reference block is determined first, and from the image upper left corner, the image block of first 8 × 8 is opened
Begin as first reference block, the position of next reference block is three pixels of translation to the right or downwards, using each reference block in
39 × 39 region of the heart is the neighborhood where current reference block, all with referring to the identical image blocks of block size all in neighborhood
It is candidate blocks, traverses candidate blocks all in neighborhood and its Euclidean distance between current reference block is obtained, select 16 Europe
The minimum candidate blocks of formula distance form a grouping as one group of similar block, this group of similar block with corresponding reference block.
The method for solving of Euclidean distance is：
In formula (1), dnoisyRepresent Euclidean distance, | | | |2Represent l-2 normal forms, ZxRRepresent the pixel value of reference block, ZxGeneration
The pixel value of candidate block in table neighborhood,Represent the pixel number in an image block.
Step 3 will respectively be grouped image block and carry out collaboration filtering and noise reduction in step 2；
Step 3.1, all image blocks are required for carrying out local two-dimensional wavelet transformation first, then by being referred in each grouping
Whether the position of the central pixel point of block in W carries out three-dimensional collaboration filtering and noise reduction to select step a or step b, and estimation is each
The sparse coefficient of image block；
If a. the position of current group internal reference block central pixel point is in W, formula (2) in NCSR models pair is used
This group of image block carries out third dimension collaboration filtering；
If b. the position of current group internal reference block central pixel point is not in W, the formula (3) in NCSR models is used
To carry out this group of image block third dimension collaboration filtering；
In formula (2), (3),Represent the estimated value to image block sparse coefficient, α represents the sparse coefficient of image block, β tables
Show the average coefficient value of one group of image block, l1=c1λ, l2=c2γ, c1And c2All it is constant；
Step 3.2, after carrying out collaboration filtering to the sparse coefficient value of image block by step 3.1, the image that is each grouped
Block all carries out 2-d wavelet inverse transformation and obtains the pixel value on its spatial domain.
Grouping image block solution after step 3 denoising is formed multiple images block by step 4, and each image block that is grouped need to return to original
Position in image will appear the image block estimated value from different grouping at certain positions of original image, and therefore, it is necessary to will
These image blocks with same coordinate are polymerize to obtain final Image estimation value by average weighted mode；
Step 4.1, the weight for obtaining multiple estimated values at same position：
In formula (4), NxRFor the number for multiple estimated values that same position occurs, σnFor original image noise variance；
Step 4.2, acquired using formula (5) it is after image block polymerization after final denoising as a result,
In formula (5),For the pixel estimated value that an image block obtains after non local filtering, xRFor in image
A reference block, xmFor one group of image some similar block in the block,For xmThe square features function at place,For the estimated value after final image denoising.
Below using the three-dimensional collaboration filtering and noise reduction method based on NCSR models to the gray scale of Cameraman (256 × 256)
Figure is handled, as shown in Figure 2.After adding in Gaussian noise, as shown in figure 3, from left to right σnValue be respectively 10,50,70,
100, for the third width noisy image (σ of Fig. 3n=70) specific denoising process is as follows：
The edge pixel containing noise image is extracted using Canny operators, and the coordinate of edge pixel is preserved
Into W；As shown in figure 4, Cameraman (256 × 256) is from left to right followed successively by, House (256 × 256), Lena (512 ×
512), Peppers (256 × 256), wherein white pixel point represent edge pixel, and black pixel point represents smooth pixel.
Alphabetical " Ra " is indicated in Fig. 5 to represent two different reference blocks with the box of " Rb " and refer to the two
Dotted line frame centered on block represents the neighborhood of the two reference blocks respectively.The image of " a ' " and " b ' " are indicated in the two neighborhoods
Block represents the most like similar block of the corresponding reference block chosen from candidate block respectively, they by with corresponding reference block
Form similar grouping；
During Block- matching is grouped, from the image upper left corner, the image BOB(beginning of block) of first 8 × 8 is first reference
Block, the position of next reference block is translates to the right or downwards three pixels.39 × 39 area centered on each reference block
Domain is the neighborhood where current reference block, and all image blocks identical with reference block size are candidate blocks in neighborhood, specifically such as
Shown in Fig. 5.Black box is image size, and black dotted lines frame is past for image symmetric replication centered on edge or image vertex
Pixel is the part that neighborhood supplement is provided for edge reference block；
Wherein, Block- matching grouping needs to traverse all candidate blocks in neighborhood and itself and current reference is obtained according to formula (1)
Euclidean distance between block, and it is stored in array G together with the coordinate of each candidate blocksm,nIn.M represents which reference block, n
Which similar block in expression group.In array Gm,nIn, it is ranked up according to the size of Euclidean distance, 16 distances before only retaining
The information of minimum similar block is in Gm,nIn, the grouping that Block- matching is formed is as shown in Figure 6.
Gm,nIn all image block carry out Local Wavelet Transform.After transformation, image block is A={ α by rarefaction representationi,j,i
=1,2, h }, which similar block wherein in i expressions group, j represent which sparse coefficient in image block.
For each group of image block：Using formula (6), the non-local mean β at every group of similar block same position is obtainedj。
In formula (6), ωiFor weight of each similar block in group, it is inversely proportional with Euclidean distance, calculation
For：
The length of sides of the N for image block, N=8.
Matching error E={ the α of image block are obtained according to above-mentioned formulai,j-βj, i=1,2 ..., h } and set A in
Standard deviation sigma and set E in standard deviation δ.
WhereinWithThe average value of respectively set A and set E, h are the number of element in set.
The value of regularization parameter λ and γ is obtained respectively using formula (10) and (11).
Estimate the sparse coefficient of each image block, method of estimation is as follows：
The centre coordinate of the grouping internal reference block is judged whether in array W, if in array W, using by formula (12)
The formula (2) derived is estimated；
If the centre coordinate of reference block not in W, is counted using by formula (13) and its derivation formula (3)
It calculates.
In formula (12), (13),For sparse coefficient estimated value,For 2-d wavelet inverse transformation, α is after wavelet transformation
Sparse coefficient, λ and γ are constant, and β is the weighted average coefficients at same position in one group of similar block；
In formula (2), (3), l1=c1λ, l2=c2γ, c1And c2All it is constant.
All image blocks carry out wavelet inverse transformation and obtain the pixel value on its spatial domain.
All image blocks return to the position in original image, in the position it is possible that there are other estimations from different grouping
Value, then will polymerize all estimated values of the position.The specific of final estimated value at the position asks the method to be：
The weight of multiple estimated values at same position is obtained first：
In formula (4), NxRFor the number for multiple estimated values that same position occurs, σnFor original image noise variance.
The result after image block polymerize after final denoising is acquired using formula (5)：
In formula (5),For the pixel estimated value that an image block obtains after non local filtering, xRFor in image
A reference block, xmFor one group of image some similar block in the block,For xmThe square features function at place,For the estimated value after final image denoising.
By Gaussian noise (σn=70) the results are shown in Figure 7 after Cameraman (256 × 256) image denoising of pollution,
For the output result after denoising of the present invention.Fig. 8 is that the present invention and the denoising result of BM3D algorithms compare, it can be seen that utilizes this calculation
Result after method denoising, visually without very big difference, but significantly compares in smooth part and BM3D in edge details part
BM3D is apparent, and ring and halo effect significantly reduce.The left side one is classified as the denoising result of BM3D in Fig. 8, and the right one is classified as
The denoising result of the present invention, it can be seen that the denoising result marginal portion of the present invention is apparent in the small box gone out from every width icon
Some.Fig. 9 is the comparison diagram of the invention with the denoising result of Denoising Algorithm outstanding in recent years, and piece image is clean
Cameraman (256 × 256) image, the second width are noisy image (σn=100), third width is the denoising result of BM3D algorithms
(PSNR=22.81), the 4th width is the denoising result (PSNR=23.28) of LINC algorithms, and the 5th width is the denoising of PCLR algorithms
As a result (PSNR=23.48), denoising result (PSNR=23.60) of the 6th width for the present invention, it is seen that the present invention is thin to edge
The processing of section still has stronger competitiveness.
After table 1 gives the denoising that the present invention and other algorithms are polluted different images by different degrees of Gaussian noise
PSNR values (i.e. Y-PSNR).In most cases, Y-PSNR of the invention is all higher than other algorithms.The present invention
0.3 decibel of average PSNR value BM3D high, it is 0.35 decibel higher than PCLR algorithm than 0.42 decibel of LINC high.The present invention's goes
Effect of making an uproar is essentially the same in smooth region and other algorithms, but it has apparent advantage to the processing of details, can allow thin
It saves more image and reaches better denoising effect.
The PSNR values comparison of the different Denoising Algorithms of table 1
By the above-mentioned means, the three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models divides noisy image
Regional processing (is divided into fringe region and smooth domain), further improves image detail part (such as：Texture, edge etc.) it is clear
Clear degree.Three-dimensional collaboration filtering and noise reduction method the present invention is based on NCSR models utilizes the Filtering Formula in NCSR models to noise
It is filtered, takes full advantage of the non local similitude of image, hence it is evident that reduce the halation and ringing effect in denoising result.
Claims (5)
1. the three-dimensional collaboration filtering and noise reduction method based on NCSR models, which is characterized in that be specifically implemented according to the following steps：
Step 1, using Canny operator extraction noisy image edge pixel points, the coordinate of the edge pixel point is stored in array W
In；
Noisy image in step 1 is grouped by step 2 by way of Block- matching, obtains multiple grouping image blocks；
Step 3 will respectively be grouped image block and carry out collaboration filtering and noise reduction in step 2；
Grouping image block solution after step 3 denoising is formed multiple images block by step 4, for having same seat in original image
Each image block of target is polymerize by average weighted mode, acquires the final estimated value of image.
2. the three-dimensional collaboration filtering and noise reduction method based on NCSR models as described in claim 1, which is characterized in that described in step 2
The specific steps are：The position of reference block is determined first, and from the image upper left corner, the image BOB(beginning of block) of first 8 × 8 is first
Reference block, the position of next reference block are to translate three pixels to the right or downwards, 39 × 39 centered on each reference block
Region be the neighborhood where current reference block, all image blocks identical with referring to block size are all candidate blocks in neighborhood,
It traverses candidate blocks all in neighborhood and its Euclidean distance between current reference block is obtained, select 16 Euclidean distance minimums
Candidate blocks as one group of similar block, this group of similar block and corresponding reference block form a grouping.
3. the three-dimensional collaboration filtering and noise reduction method based on NCSR models as claimed in claim 2, which is characterized in that it is described it is European away from
From method for solving be：
In formula (1), dnoisyRepresent Euclidean distance, | | | |2Represent l-2 normal forms, ZxRRepresent the pixel value of reference block, ZxRepresent neighbour
The pixel value of candidate block in domain,Represent the pixel number in an image block.
4. the three-dimensional collaboration filtering and noise reduction method based on NCSR models as described in claim 1, which is characterized in that step 3 is specific
Step is：
Step 3.1, all image blocks are required for carrying out local two-dimensional wavelet transformation first, then by reference block in each grouping
Whether the position of central pixel point in W carries out three-dimensional collaboration filtering and noise reduction to select step a or step b, estimates each image
The sparse coefficient of block；
If a. the position of current group internal reference block central pixel point is in W, using formula (2) in NCSR models come to the group
Image block carries out third dimension collaboration filtering；
If b. the position of current group internal reference block central pixel point is not in W, the formula (3) in NCSR models pair is used
This group of image block carries out third dimension collaboration filtering；
In formula (2), (3),Represent the estimated value to image block sparse coefficient, α represents the sparse coefficient of image block, and β represents one
The average coefficient value of group image block, l1=c1λ, l2=c2γ, c1And c2All it is constant；
Step 3.2, after carrying out collaboration filtering to the sparse coefficient value of image block by step 3.1, the image block that is each grouped
It carries out 2-d wavelet inverse transformation and obtains the pixel value on its spatial domain.
5. the three-dimensional collaboration filtering and noise reduction method based on NCSR models as described in claim 1, which is characterized in that described in step 4
The specific of the final estimated value of image asks the method to be：
Step 4.1, the weight for obtaining multiple estimated values at same position：
In formula (4), NxRFor the number for multiple estimated values that same position occurs, σnFor original image noise variance；
Step 4.2, acquired using formula (5) it is after image block polymerization after final denoising as a result,
In formula (5),For the pixel estimated value that an image block obtains after non local filtering, xRFor one in image
A reference block, xmFor one group of image some similar block in the block,For xmThe square features function at place,For
Estimated value after final image denoising.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110060220A (en) * | 2019-04-26 | 2019-07-26 | 中国科学院长春光学精密机械与物理研究所 | Based on the image de-noising method and system for improving BM3D algorithm |
| CN113487501A (en) * | 2021-06-29 | 2021-10-08 | 嵊州市浙江工业大学创新研究院 | Novel underwater image restoration method based on dark channel prior and BM3D algorithm |
-
2017
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Non-Patent Citations (1)
| Title |
|---|
| JING LIU ET AL: "《Collaborative filtering denoising algorithm based on the nonlocal centralized sparse representation model》", 《2017 10TH INTERNATIONAL CONGRESS ON IMAGE AND SIGNAL PROCESSING, BIOMEDICAL ENGINEERING AND INFORMATICS (CISP-BMEI)》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110060220A (en) * | 2019-04-26 | 2019-07-26 | 中国科学院长春光学精密机械与物理研究所 | Based on the image de-noising method and system for improving BM3D algorithm |
| CN113487501A (en) * | 2021-06-29 | 2021-10-08 | 嵊州市浙江工业大学创新研究院 | Novel underwater image restoration method based on dark channel prior and BM3D algorithm |
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