Some Studies About Piecewise Constant Signal And Image Denoising

In the signal and image processing,piecewise constant siganls and images are an important kind of data,which are widely used in both general commercial and automo-tive industry use.Typical examples include bar code signals,Quick Response codes,logos,cartoons and text images.Each of them consists of some different homogeneous regions separated by distinct edges.However,due to the limitation of the acquisition and transmission,they are unavoidable to be degraded by noise.Thus,the quality of ob-served siganls and images are usually bad.Compared to other kinds of noise,Gaussian noise is the most important one.It is a basic and significant task to remove noise from the damaged data.This work can not only improve the quality of data,but also pro-vide more reliable information for subsequent processing(such as image segmentation,compression,recognition,etc.).In the thesis,a series of selective weighted averaging algorithms are proposed to repair piecewise constant signals and images corrupted by Gaussian noise.To preserve the characteristics of edges,we first adopt the Neumann boundary condition at edges.It prevents the diffusion between different homogeneous regions thoroughly.We elab-orate the contents of this thesis from the following aspects:In the first chapter,we first introduce the basic concepts of signal and image de-noising,the current research situation and the main problems.Then,we review the existing algorithms related to this thesis.At last,we give the content arrangement.In the second chapter,a novel method based on selective averaging and outlier removal is proposed for signal and image denoising.To see the essential idea clearly,we first present our method for 1D signal and also provide some theoretical results.This algorithm works pretty well,when the noise level is low.However,there are some noisy pixels left in the output when eliminating the high level of noise.To solve this problem,a simple and effective strategy is adopted to detect and suppress these sparse outliers.The whole algorithm for 2D gray image can be regarded as a straightforward extension of that for 1D signal.Experiments on both gray and color image denoising show that our method is able to obtain satisfactory results,which are very close to the clean iamges.In the third chapter,we propose a general selective averaging method.Theoreti-cally,we can prove the convergence of this algorithm.By using the properties of finite Markov chains,we provide a probabilistic interpretation.Moreover,from these two aspects,we compare our method to the iterated neighborhood filter.For the choice of weight parameters,we discuss its influence on the asymptotic rate of convergence and also study its influence on the denoising results with a moderate number of iterations.In 2D case,we propose a novel extension called the alternating general selective aver-aging method.A numerical verification of its convergence is provided.The proposed algorithm is not only better than traditional methods,but also the previous method in-troduced in second chapter.However,when the noise level is high,this method still leads to sparse outliers.In the fourth chapter,we propose a selective averaging method with multiple neigh-bors to reduce the noisy pixels appearing in the final result when dealing with the high level noise.The algorithm averages more homogeneous neighbors selected from a large domain,which is based on the property of the local geometry of signals and images.By carefully designing the average scheme,our method can guarantee the convergence of the denoised signal sequence.Compared to the general selective averaging method,this algorithm achieves superior performance visually and quantitatively.Furthermore,it also needs less iterations and time consumption.At last,we try to use our algorithm to restore noisy images corrupted by speckle noise.The fifth chapter summarizes this thesis and gives some future work.