Image De-noising Algorithm Via Stationary Wavelet-domain Wiener Filter Based On Correlation Model

1. Introduction In the field of medical imaging and image processing, it is one of the importantreasons that noise depresses the quality of the image. For the sake of improving thequality of the image and doing further image compression and fractals processing,it's resolutely necessary to de-noise image. De-noising image has a dilemmaproblem which is how to keep balance in debasing noise and keep image edge. Theconventional low-pass filtering method strain the high frequency part, debase noise.But they destroy image edge. So it is a hotspot problem that De-noise image aswell as keep image edge. Wavelet transform is a cogent tool of mathematics analysis, which come in forattention widely in recent years and applied in many image processing domain.Wavelet domain de-noising can be generally divided into wavelet shrinkage,projection method and correlation method. Now wavelet shrinkage is the widestresearched method. Wavelet shrinkage divides into threshold shrinkage and ratioshrinkage. Projection method has tow kinds: Matching Pursuits and MCD(Multiple Compact Domain) or POCS (Projection onto Convex Set). Correlationmethod is applied in de-noising, based on the dependency of signal coefficients inscale and across scales, but the coefficients of the noise are feeble or independent.Our method confirms the direction of study, based on the characteristic of signaland noise in wavelet domain, and establishes an exponentially decayingautocorrelation model of nature image.2. Stationary wavelet transform Wavelet transform can present signal information in time (spatial)-domain and ８０　Abstractfrequent-domain. So there are tow choices of space and frequency for de-noising inwavelet domain. Many wavelet image de-noising algorithms process subband noisein threshold after using orthogonal wavelet decomposing signal and noise, expectto obtain impressive de-noising performance. But threshold de-noising based onorthogonal wavelet transform make the reconstructed image edge surge, lead toimage edge distortion. Especially there is strong noise in image, it blurreconstructed image after threshold processing of multilayer detail image. Stationary wavelet transform is one kind of nonorthogonal wavelet transformon the basis of orthogonal wavelet transform, and has the characteristic ofredundancy and shift-invariability, so it is adaptive to process correlation problem.Image threshold de-noising based on Stationary wavelet transform can strain imageGibbs surge in orthogonal wavelet transform domain, keep the characteristic ofimage edge and visual quality well. Signal Stationary wavelet decomposition is ?????Cj+1 = dε HCj +1 Dj = dεGCjThe above formula indicate that signal doesn't be downsampled in the process ofthe stationary wavelet transform, the length of the approaching signal and detailsignal is same as the original signal's. Inverse transform of the stationary wavelettransform is aj ε1,L,ε = ( ) 1 [R[ (a j] ) [ j]( )] j ,bj + R1 aj ,bj 2 0 j+1 +1 +1 +1The reconstruction of signal based on Stationary wavelet transform is to reconstructsignal separately according to the even sample and odd sample of transformcoefficients first, then average them.3. Image de-noising via stationary wavelet-domain Wiener filter based on correlation model ８１　吉林大学硕士学位论文　 It has been observed with some consistency that the wavelet coefficients ofnatural images have a clustering property in the same scale. In other words, awavelet coefficient's magnitude is not independent of its neighbors. Thisdependency decays quickly with distance. We propose an exponential decay modelacc...