CN107067376A - A kind of RBF interpolation the images with salt and pepper noise restorative procedure - Google Patents
A kind of RBF interpolation the images with salt and pepper noise restorative procedure Download PDFInfo
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Abstract
To improve the images with salt and pepper noise repairing quality, the present invention discloses a kind of RBF interpolation the images with salt and pepper noise restorative procedure.Basic skills is：Pixel in noise image is divided into pollution pixel and uncontaminated pixel, pollution pixel valuation problem look at the unorganized points problem based on uncontaminated pixel；Using RBF unorganized points methods, with uncontaminated pixel image coordinate, pixel value training RBF model parameters, to pollute pixel image coordinate as input, using RBF interpolation methods estimation pollution pixel value, the pixel value of pollution pixel is replaced, the images with salt and pepper noise reparation is realized.The method have the advantages that：High density salt-pepper noise pollution image signal to noise ratio can be significantly increased.
Description
Technical field
The present invention relates to digital image processing techniques field, a kind of RBF interpolation the images with salt and pepper noise restorative procedure is refered in particular to.
Background technology
Digital imagery sensor CCD or CMOS etc. are widely used in the field such as industry, amusement, civilian, in actual use
During, influenceed by factors such as manufacturing defect, device aging, errors of transmission, there is the spiced salt in the image of acquisition makes an uproar
Sound pollution.Salt-pepper noise often shows as constant incandescent or very dark pixel, so that span is 0-255 gray level image as an example,
The value of salt-pepper noise pixel is usually 255 or 0.This noise can significantly reduce picture quality, seriously reduce visual effect.Such as
Shown in Fig. 1,1 is original image, and 2 be 30% salt-pepper noise pollution image.Salt-pepper noise influences maximum to picture quality, and some are non-
Linear filter method is used for the images with salt and pepper noise denoising.Medium filtering is used for the images with salt and pepper noise denoising earliest, and it is with picture
Mesophyticum replaces current pixel in plain neighborhood, carries out image filtering, Fig. 3 is 2 median-filtered result.Because medium filtering can be by not
Replaced with pixel median in neighborhood with polluting pixel error, and filtered image is produced distortion.Therefore, Sun etc.（[Sun, T,
Neuvo, Y., 1994. Detail-preserving median based filters in image processing.
Pattern Recognition Lett. 15 (4), 341–347.）Switching median filter is proposed first（Switching
Median Filter, SMF).SMF basic thought is：Pollution pixel is first marked in contaminated image（Such as pixel value
It is pollution pixel for 255 or 0 pixel）With uncontaminated pixel（Pixel of the pixel value between 0-255）；In image repair
During, only pollution pixel is handled, uncontaminated pixel keeps constant.So ensure that uncontaminated pixel not by neighborhood
Interior pixel median is substituted, and with more high fidelity.4 be 2 switching median filter results, it can be seen that switching median filter
As a result it is substantially better than traditional median filter method.But, when salt-pepper noise contamination density is larger, such as in more than 80%, Fig. 1
5, medium filtering and switching median filter are all difficult to obtain comparatively ideal reparation image.As shown in figure 1,6 be 5 medium filtering knot
Really, 7 be 5 selection median-filtered result.
High density（Salt-pepper noise Contamination ratio is more than 50%）Salt-pepper noise pollution image Denoising Problems are received both at home and abroad
Scholar's extensive concern.Such as, Esakkirajan (2011) etc.（Esakkirajan S, Veerakumar T,
Subramanyam AN, PremChand CH. Removal of high density salt and pepper noise
through modified decision based unsymmetric trimmed median filter. IEEE
Signal Process Lett 2011;18(5):287–90.）Propose that asymmetric tri-state is filtered for repairing the height density spiced salt
Image polluted by noise.Lu（2012）Deng（Lu C.-T, Chou T.-C. Denoising of salt-and-pepper
noise corrupted image using modified directional-weighted-median filter,
Pattern Recognition Letters, vol. 33, no. 10, pp.1287–1295,2012.）Propose improved side
To Weighted median filtering algorithm, available for 80% salt-pepper noise pollution image of reparation.Mu（2013）Deng（Mu H H, Fan C C,
et al. Fast and efficient median filter for removing 1-99% levels of salt-
and-pepper noise in images. Engineering Applications of Artificial
Intelligence.26 (2013) 1333-1338）According to different noise density grades, SMF algorithm search windows are improved big
A kind of small and direction, it is proposed that quick, high density salt-pepper noise elimination algorithm, can be achieved 99% salt-pepper noise pollution image and repairs.
Vijaykumar（2014）Deng（V.R.Vijaykumar, G.Santhana, et al. Fast switching based
median-mean filter for high density salt and pepper noise removal.
International Journal of Electronics and Communications.p:1145–1155,2014）Propose
A kind of selection average median filtering algorithm, by increasing the size of search window, can be achieved 90% salt-pepper noise pollution image and repaiies
It is multiple.Zhang（2014）Deng（Zhang C, Wang K. et al. Removal of high-density impulse
noise based on switching morphology-mean filter.International Journal of
Electronics and Communications.2014）Morphology is merged with selection filtering, selection Mathematical morphology filter is proposed
Ripple, open and close morphologic filtering is selected by 2 layer choosings, and 90% salt-pepper noise pollution image can be achieved and repairs.But, it is this kind of based on local
Intermediate value, average, extreme value in window（Maximum or minimum value）Selection filtering method, carry out high density the images with salt and pepper noise repair
When multiple, it is fuzzy that larger filter window easily produces image, and then reduces signal noise ratio (snr) of image after reparation.In addition, existing method
It is general using pixel in detection image is most bright or most dark pixel by the way of, detection salt-pepper noise.This detection mode, easily by position
Uncontaminated pixel in brighter or darker area is mistaken for noise pollution pixel.
The content of the invention
For further lifting the images with salt and pepper noise repairing quality, the present invention provides a kind of RBF interpolation the images with salt and pepper noise and repaiied
Compound method.The technical scheme that the present invention is provided is：Pixel p in the images with salt and pepper noise I is first divided into pollution pixel e and uncontaminated
Pollution pixel e valuation problem, look at the unorganized points problem based on uncontaminated pixel t by pixel t；Using RBF scattered points
Interpolation method, with uncontaminated pixel t image coordinate xtWith pixel value qtRBF models are trained, to pollute pixel e image coordinates xeMake
For input, pollution pixel e pixel value q is estimated using RBF interpolation methodse', replace pollution pixel e pixel value qe, realize green pepper
Salt noise image is repaired；
Concrete operation step is as follows：
The first step：Carry out image salt-pepper noise detection
The given the images with salt and pepper noise I that a width size is w*h pixel, bit wide is b bit, picture traverse w spans are 1
~ 100000000, picture altitude h span are 1 ~ 100000000, and image bit wide b spans are 1 ~ 100, the figure of pixel p
Picture coordinate is x, x=(u, v), and (u, v) is pixel transverse and longitudinal coordinate, and pixel value is q；
The specific method for carrying out pollution pixel detection in the images with salt and pepper noise I is as follows：
1.1st step, is sized all elements in the mark matrix F for w*h, F (u, v) and is set as 1, (u, v) is image transverse and longitudinal
Element span is 0 ~ 100 in coordinate, setting salt-pepper noise detection threshold value A={ a1, a2, a3, a4, a5, a6 }, A；Set picture
Plain brightness detection threshold value m, span is 0 ~ 2b-1；Set neighborhood similarity detection threshold value, span is 0 ~ 2b-1；If
Initial value d, the d span for determining neighborhood size L are 0 ~ 100；
1.2nd step, takes pixel p (u, v) in the images with salt and pepper noise I, and its pixel value is q (u, v), when
When, turn the 1.8th step；
1.3rd step, setting neighborhood size L=d calculates salt-pepper noise detection metric N1(u,v)、N2(u,v)：
Formula (1)
Formula (2)
Wherein, S1It is that bright pixel quantity, P are crossed in pixel q (u, v) neighborhood1Be in current pixel neighborhood with current pixel difference compared with
Small non-bright pixel quantity excessively；S2It is that dark pixel quantity, P are crossed in current pixel neighborhood2It is in current pixel neighborhood and current pixel
The less non-dark pixel quantity excessively of difference；
Formula (3)
Formula (4)
e1Represent that the pixel was bright pixel equal to 1；
Formula (5)
Formula (6)
g1Represent that the pixel crosses bright pixel to be non-equal to 1, and it is smaller with pixel difference at (u, v) position；
Formula (7)
Formula (8)
E2 is equal to 1 and represents that the pixel was dark pixel；
Formula (9)
Formula (10)
g2Represent that the pixel crosses dark pixel to be non-equal to 1, and it is smaller with pixel difference at (u, v) position；
Formula（1-10）In, RL(u, v) be using centered on pixel p (u, v), size as（2L+1）*（2L+1）Local neighborhood,It is pixel coordinate in local neighborhood, span is 1 ~ 2L+1；
1.4th step, works as N1(u,v)>=a1And N2(u,v)>=a2Or N1(u,v)+N2(u,v)>=a3When, turn the 1.8th step；
1.5th step, setting neighborhood size parameter L=d+1, by formula（1-10）N is calculated again1(u,v)、N2(u,v);
1.6th step, works as N1(u,v)>=a4And N2(u,v)>=a5Or N1(u,v)+N2(u,v)>=a6When, turn the 1.8th step；
1.7th step, setting F (u, v)=0；
1.8th step, returns to the 1.2nd step, until all pixels are processed in the images with salt and pepper noise I；
According to mark matrix F, all pixels p (u, v) in traversal the images with salt and pepper noise I, as F (u, v)=1, by this element marking
For pollution pixel e, pollution pixel e pixel coordinate is xe, pixel value be qe；As F (u, v)=0, by this pixel labeled as not dirty
The pixel coordinate for contaminating pixel t, uncontaminated pixel t is xt, pixel value be qt；All pollution pixel e constitute pollution set of pixels, the uncontaminated set of pixels of all uncontaminated pixel t compositions, m, n value
Scope is [0 ~ w*h], n=w*h-m；
Second step：RBF interpolation models are built, uncontaminated set of pixels is usedTrain RBF interpolation models
Parameter；
2.1st step：Build RBF interpolation models：
Formula（11）
Wherein,It is k-th of pollution pixel ekEstimation pixel value, k span is [1 ~ m],It is uncontaminated i-th
Pixel tiImage coordinate, i span is [1 ~ n],It is model parameter,
It is interpolating function, interpolating functionIncluding：
Gaussian function：
Formula（12）
Quadratic function：
Formula（13）
Linear function：
Formula（14）
Cubic function：
Formula（15）
Trigonometric function：
Formula（16）
Wherein,It is Gauss, quadratic function parameter, span is [0 ~ 100],It is i-th of uncontaminated picture
Plain tiWith k-th of pollution pixel ekImage pixel coordinates Euclidean distance；
2.2nd step：Use uncontaminated set of pixelsCalculate RBF interpolation model parameters：
Use uncontaminated set of pixelsImage coordinate, pixel value,
Build n linear equation：
Formula（17）
The optimized parameter of estimator (17)；
3rd step：Pollution set of pixels E pixel coordinate is substituted into RBF interpolation models, the pixel value of estimation pollution pixel；
Pollution set of pixelsPixel coordinateThe RBF for substituting into formula (18) successively is inserted
It is worth model, calculate the pixel value of pollution pixel
Formula（18）
4th step：WillInstead of corresponding position pixel in the images with salt and pepper noise I, complete pollution image and repair
It is multiple.
Beneficial effect of the present invention：
1）The noise detecting method proposed, can effectively overcome existing method by the use of most bright or most dark pixel as detector, draw
The error detection risen.In the present invention, noise measuring is by crossing bright pixel in neighborhood, crossing dark pixel, non-cross dark pixel, non-excessively bright
The statistical information of pixel is more rationally and effective compared to the simple brightness value using a pixel as comprehensive criterion.
2）Reparation signal noise ratio (snr) of image is remarkably improved, the vision visual information of image is repaired in enhancing.As shown in Fig. 2 with big
Small is that the Lena gray level images that 1024*1024 pixels, pixel depth are b=8bits carry out test assessment, and picture noise density is
90%, repair algorithm with existing salt-pepper noise and contrasted, interpolation kernel function selection line function in the inventive method.Participation pair
The existing the images with salt and pepper noise restorative procedure of ratio includes：Medium filtering, Weighted median filtering（WMF, Yin L, Ruikang
Yang, Moncef Gabbouj, Yrjo Neuvo. Weighted median filters: tutorial. IEEE
Trans Circuits Syst II 1996;43(3):157-92.), Center Weighted median is filtered（CWMF, Ko S-J, Lee
YH. Center weighted median filters and their applications to image
enhancement. IEEE Trans Circuits Syst 1991.38(9):984–93.）, adaptive Center Weighted median
Filtering（ACWMF, Chen T, Wu HR. Adaptive impulse detection using center-weighted
median filters. IEEE Signal Process Lett 2001;8(1):1–3.）, improve selection medium filtering
（PSMF, Wang Z, Zhang D. Progressive switching median filter for the removal of
impulse noise from highly corrupted images. IEEE Trans Circuits Syst II 1999;
46(1):78–80.）, adaptive median filter（AMF, Hwang H, Haddad RA. Adaptive median filters:
new algorithms and results.IEEE Trans Image Process 1995;4(4):499–502.）, border
Differentiate noise measuring（BDND, Ng P-E, Ma K-K. A switching median filter with boundary
discriminative noise detection for extremely corrupted images. IEEE Trans
Image Process 2006;15(6):1506-16.), based on decision making algorithm（DBA, Srinivasan KS, Ebenezer
D. A new fast and efficient decision-based algorithm for removal of high-
density impulse noises. IEEE Signal Process Lett. 2007;14(3):189–92.）, it is simple from
Adapt to medium filtering（SAMF, Haidi I, Nicholas SPK, Theam FN. Simple adaptive median
filter for removal of impulse noise from highly corrupted images. IEEE Trans
Consum Electron 2008;54 (4)), improve the asymmetric tri-state medium filtering based on decision-making（DBUTMF,
Esakkirajan S, Veerakumar T, Subramanyam AN, PremChand CH. Removal of high
density salt and pepper noise through modified decision based unsymmetric
trimmed median filter. IEEE Signal Process Lett 2011;18(5):287–90.）, average intermediate value
Filtering algorithm（SMMF, V.R.Vijaykumar, G.Santhana, et al. Fast switching based median-
mean filter for high density salt and pepper noise removal. International
Journal of Electronics and Communications [J]. (2014)1145–1155）, and the present invention is in fact
Apply example 1 and repair result.From Fig. 2, it can be seen that the embodiment of the present invention 1 repairs result and remains more image details, effect is repaired
Fruit is substantially better than AMF, BDND, DBA, SAMF, MMF, SMMF scheduling algorithm.Fig. 3 gives the inventive method in 99% noise density
In the case of repair result, embody the inventive method and possess good repair ability to high density image polluted by noise.
Brief description of the drawings
Fig. 1 the images with salt and pepper noise pollutes and existing method denoising result.
When Fig. 2 noise densities are 90%, inventive algorithm is with existing algorithm pattern as repairing effect is contrasted.
The noise density pollution image the inventive method of Fig. 3 99% repairs result.
In figure, 1 is original image, and 2 be 30% salt-pepper noise pollution image, and 3 be 2 median-filtered result, and 4 be 2 selection
Median-filtered result, 5 be 80% salt-pepper noise pollution image, and 6 be 5 median-filtered result, and 7 be 5 selection medium filtering knot
Really, 8 be 90% salt-pepper noise pollution image, and 9 be 8 median-filtered result, and 10 be 8 WMF results, and 11 be at 8 CWMF
Result is managed, 12 be 8 ACWMF results, and 13 be 8 PSMF results, and 14 be 8 AMF results, and 15 be 8
BDND results, 16 be 8 DBA results, and 17 be 8 SAMF results, and 18 be 8 DBUTMF results, 19
Be 8 SMMF results, 20 be the inventive method result.
Embodiment
Present invention is described further with reference to the accompanying drawings and examples.
Embodiment 1
Selection size is the Lena gray level images that 1024*1024 pixels, pixel depth are b=8bits, in Matlab2014a platforms
Experiment is estimated, salt-pepper noise pollution image I is generated using imnoise functional simulations in matlab, noise density is 90%.
The first step：Carry out image salt-pepper noise detection
1.1st step, is sized all elements in the mark matrix F for 1024*1024, F (u, v) and is set as 1, and setup parameter A=
{ 2,7,7,4,16,18 }, setup parameter m=5, setup parameter=5, setup parameter d=1；
1.2nd step, whenWhen, turn the 1.8th step；
1.3rd step, setting neighborhood size parameter L=d, is calculated：
Wherein,
Formula (1)
Formula (2)
Formula (3)
Formula (4)
Formula (5)
Formula (6)
Formula (7)
Formula (8)
Formula (9)
Formula (10)
Formula（1-10）In,It is image pixel transverse and longitudinal coordinate,Be using centered on pixel q (u, v), size as（2L+
1）*（2L+1）Local neighborhood,It is pixel coordinate in local neighborhood, span is 1 ~ 2L+1；
1.4th step, whenAnd, orWhen, turn the 1.8th
Step；
1.5th step, setting neighborhood size parameter L=d+1, by formula（1-9）Calculate again;
1.6th step, whenAnd, orWhen, turn the 1.8th step；
1.7th step, setting F (u, v)=0；
1.8th step, returns to the 1.2nd step, until all pixels are traversed in image I；
According to mark matrix F, traversing graph works as F as all pixels p in I（u,v）When=1, by this pixel labeled as pollution pixel e,
The pixel coordinate for polluting pixel e is xe, pixel value be qe；Work as F（u,v）When=0, this pixel is labeled as uncontaminated pixel t, it is not dirty
The pixel coordinate for contaminating pixel t is xt, pixel value be qt；All pollution pixel e constitute pollution set of pixels, institute
There is uncontaminated pixel t to constitute uncontaminated pixelCollect, m, n span are：[0 ~ w*h], n=w*h-m；
Second step：RBF interpolation models are built, uncontaminated pixel is usedCollection training RBF interpolation model parameters；
2.1st step：Build RBF interpolation models：
Formula（11）
Wherein,It is k-th of pollution pixel ekEstimation pixel value, k span is [1 ~ m],It is uncontaminated i-th
Pixel tiImage coordinate, i span is [1 ~ n],It is model parameter,It is slotting
Value function, interpolating functionIncluding：
Gaussian function：
Formula（12）
Quadratic function：
Formula（13）
Linear function：
Formula（14）
Cubic function：
Formula（15）
Trigonometric function：
Formula（16）
Wherein,It is Gauss, quadratic function parameter, span is [0 ~ 100],It is i-th of uncontaminated pixel ti
With k-th of pollution pixel ekImage pixel coordinates Euclidean distance；
2.2nd step：Use uncontaminated set of pixelsCalculate RBF interpolation model parameters：
Use uncontaminated set of pixelsImage coordinate, pixel value, structure
Build n linear equation：
Formula（17）
The optimized parameter of estimator (7)；
3rd step：Pollution set of pixels E pixel coordinate is substituted into RBF interpolation models, the pixel value of estimation pollution pixel；
Pollution set of pixelsPixel coordinateThe RBF interpolation of formula (18) is substituted into successively
Model, calculate the pixel value of pollution pixel
Formula（18）
4th step：WillInstead of corresponding position pixel in image I, pollution image reparation is completed.
Embodiment 2
Difference from Example 1, image pixel depth b=12bits.
Embodiment 3
Difference from Example 1, image pixel depth b=16bits.
Embodiment 4
Difference from Example 1, image pixel depth b=20bits.
Embodiment 5
Difference from Example 1, image pixel depth b=24bits.
Embodiment 6
Difference from Example 1, image pixel depth b=12bits, noise density is 99%.
Embodiment 7
Difference from Example 1, image pixel depth b=16bits, noise density is 99%.
Embodiment 8
Difference from Example 1, image pixel depth b=20bits, noise density is 99%.
Embodiment 9
Difference from Example 1, image pixel depth b=24bits, noise density is 99%.
Embodiment 10
Difference from Example 1, interpolating function selection quadratic function,。
Embodiment 11
Difference from Example 1, interpolating function selection linear function。
Embodiment 12
Difference from Example 1, interpolating function selection cubic function。
Embodiment 13
Difference from Example 1, interpolating function selection trigonometric function。
Embodiment 14
Difference from Example 1, image pixel depth b=12bits, interpolating function selection quadratic function,。
Embodiment 15
Difference from Example 1, image pixel depth b=16bits, interpolating function selection linear function。
Embodiment 16
Difference from Example 1, image pixel depth b=20bits, interpolating function selection cubic function。
Embodiment 17
Difference from Example 1, image pixel depth b=24bits, interpolating function selection trigonometric function。
Claims (1)
1. a kind of RBF interpolation the images with salt and pepper noise restorative procedure, it is characterised in that：First pixel p in the images with salt and pepper noise I is divided
For pollution pixel e and uncontaminated pixel t, pollution pixel e valuation problem look at the unorganized points based on uncontaminated pixel t
Problem；Using RBF unorganized points methods, with uncontaminated pixel t image coordinate xtWith pixel value qtRBF models are trained, to pollute
Pixel e image coordinates xeAs input, pollution pixel e pixel value q is estimated using RBF interpolation methodse', replace pollution pixel e
Pixel value qe, realize the images with salt and pepper noise reparation；
Concrete operation step is as follows：
The first step：Carry out image salt-pepper noise detection
The given the images with salt and pepper noise I that a width size is w*h pixel, bit wide is b bit, picture traverse w spans are 1
~ 100000000, picture altitude h span are 1 ~ 100000000, and image bit wide b spans are 1 ~ 100, the figure of pixel p
Picture coordinate is x, x=(u, v), and (u, v) is pixel transverse and longitudinal coordinate, and pixel value is q；
The specific method for carrying out pollution pixel detection in the images with salt and pepper noise I is as follows：
1.1st step, is sized all elements in the mark matrix F for w*h, F (u, v) and is set as 1, (u, v) is image transverse and longitudinal
Element span is 0 ~ 100 in coordinate, setting salt-pepper noise detection threshold value A={ a1, a2, a3, a4, a5, a6 }, A；Set picture
Plain brightness detection threshold value m, span is 0 ~ 2b-1；Set neighborhood similarity detection threshold value, span is 0 ~ 2b-1；If
Initial value d, the d span for determining neighborhood size L are 0 ~ 100；
1.2nd step, takes pixel p (u, v) in the images with salt and pepper noise I, and its pixel value is q (u, v), when
When, turn the 1.8th step；
1.3rd step, setting neighborhood size L=d calculates salt-pepper noise detection metric N1(u,v)、N2(u,v)：
Formula (1)
Formula (2)
Wherein, S1It is that bright pixel quantity, P are crossed in pixel q (u, v) neighborhood1It is smaller with current pixel difference in current pixel neighborhood
It is non-cross bright pixel quantity；S2It is that dark pixel quantity, P are crossed in current pixel neighborhood2It is poor with current pixel in current pixel neighborhood
Different less non-dark pixel quantity excessively；
Formula (3)
Formula (4)
e1Represent that the pixel was bright pixel equal to 1；
Formula (5)
Formula (6)
g1Represent that the pixel crosses bright pixel to be non-equal to 1, and it is smaller with pixel difference at (u, v) position；
Formula (7)
Formula (8)
E2 is equal to 1 and represents that the pixel was dark pixel；
Formula (9)
Formula (10)
g2Represent that the pixel crosses dark pixel to be non-equal to 1, and it is smaller with pixel difference at (u, v) position；
Formula（1-10）In, RL(u, v) be using centered on pixel p (u, v), size as（2L+1）*（2L+1）Local neighborhood,It is pixel coordinate in local neighborhood, span is 1 ~ 2L+1；
1.4th step, works as N1(u,v)>=a1And N2(u,v)>=a2Or N1(u,v)+N2(u,v)>=a3When, turn the 1.8th step；
1.5th step, setting neighborhood size parameter L=d+1, by formula（1-10）N is calculated again1(u,v)、N2(u,v);
1.6th step, works as N1(u,v)>=a4And N2(u,v)>=a5Or N1(u,v)+N2(u,v)>=a6When, turn the 1.8th step；
1.7th step, setting F (u, v)=0；
1.8th step, returns to the 1.2nd step, until all pixels are processed in the images with salt and pepper noise I；
According to mark matrix F, all pixels p (u, v) in traversal the images with salt and pepper noise I, as F (u, v)=1, by this element marking
For pollution pixel e, pollution pixel e pixel coordinate is xe, pixel value be qe；As F (u, v)=0, by this pixel labeled as not dirty
The pixel coordinate for contaminating pixel t, uncontaminated pixel t is xt, pixel value be qt；All pollution pixel e constitute pollution set of pixels, the uncontaminated set of pixels of all uncontaminated pixel t compositions, m, n value
Scope is [0 ~ w*h], n=w*h-m；
Second step：RBF interpolation models are built, uncontaminated set of pixels is usedTrain RBF interpolation models ginseng
Number；
2.1st step：Build RBF interpolation models：
Formula（11）
Wherein,It is k-th of pollution pixel ekEstimation pixel value, k span is [1 ~ m],It is i-th of uncontaminated picture
Plain tiImage coordinate, i span is [1 ~ n],It is model parameter,It is
Interpolating function, interpolating functionIncluding：
Gaussian function：
Formula（12）
Quadratic function：
Formula（13）
Linear function：
Formula（14）
Cubic function：
Formula（15）
Trigonometric function：
Formula（16）
Wherein,It is Gauss, quadratic function parameter, span is [0 ~ 100],It is i-th of uncontaminated picture
Plain tiWith k-th of pollution pixel ekImage pixel coordinates Euclidean distance；
2.2nd step：Use uncontaminated set of pixelsCalculate RBF interpolation model parameters：
Use uncontaminated set of pixelsImage coordinate, pixel value, build n linear equation：
Formula（17）
The optimized parameter of estimator (17)；
3rd step：Pollution set of pixels E pixel coordinate is substituted into RBF interpolation models, the pixel value of estimation pollution pixel；
Pollution set of pixelsPixel coordinateFormula (18) is substituted into successively
RBF interpolation models, calculate the pixel value of pollution pixel
Formula（18）
4th step：WillInstead of corresponding position pixel in the images with salt and pepper noise I, pollution figure is completed
As repairing.
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