基于小波变换的图像处理方法研究（主要研究图像增强，包括源代码）

苏州科技学院本科生毕业设计（论文）

in whole image,which can effectively preserve image details and textures.The nonlocal means filter produces impressive results in denoising textured patterns.A more complicated neighborhood filter based on self-similarity of image blocks was introduced by Dabov et al.,which is actually also a weighted average algorithm,just after a transform-domain collaborative filtering.This algorithm achieves state-of-the-art denoising performance in term of peak signal-to-noise ratio.

In this paper,to better preserve or enhance image detail and textures,we propose improved algorithms for image denoising and enhancement based on image decomposition by the strategy of feature-dependent adaptive processing.In order to keep the presentation of this idea simple and focused,we exploit and integrate the classic methods:the total variation regularization,the anisotropic diffusion,the shock filters and the nonlocal means filter in different combinations.A basic idea is that,two components(geometrical structure and oscillating pattern)of a given image are processed using different procedures:the geometrical variational approaches and diffusion equations are used to process the structure part(edges and details),and the nonlocal means filter is used to remove noise in the oscillating part(textures and noise).

Image smoothing and sharpening are two opposite operations in image processing.Generally speaking,image smoothing is to eliminate unnecessary and false discontinuous features(such as noise),while image sharpening is to produce or enhance some discontinuous features(such as edges and details) in proper positions of image.In many cases,image denoising methods often blur inevitably image edges and detail even if these methods are designed elaborately.For example,see following experiments on noisy images.Thus, both image smoothing and sharpening are needed simultaneously even if in a single image denoising task.One will see that,methods including the two operations obtain better visual results in experiments.

The rest of this paper is organized as follows.In section Ⅱ,we briefly review some classic works:the anisotropic diffusion,the total variation regularization methods,the shock filters,and neighborhood filters.Then,improved algorithms integrating these

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苏州科技学院本科生毕业设计（论文）

classic methods are proposed in section Ⅲ.Experiments on test images are described in section Ⅳ.Finally,conclusions are drawn out in section Ⅴ. Ⅱ.SOME CLASSIC METHODS

In this section,we review some classic methods in image denoising and enhancement.

A. Anisotropic diffusion

In order to stop smoothing of edges,Perona and Malikproposed the anisotropic diffusion equation:

?u?g(?v)?u? (1) ?div?tusing following diffusion coefficients:

?u g??u??exp?(2) (2)

Kand

g??u??1??u??1???K???22 (3)

with a gradient threshold K.The anisotropic diffusion equation contains a local backward diffusion process for bigger image gradients than K. B. Total variation

A general variational denoising algorithm is to minimize the following energy: E??????u?dx???2??f?udx (4)

2With a given image f and a regularization parameter ?.Its solution can be approximated using an artificial time marching method:

?u?d?t?'?u??i?v??u??u??????f?u? (5) ??To choose ?????? gives the classic total variation model.

In order to better preserve textural information of image,Gillboa et al.proposed an adaptive regularized total variation(ARTV) denoising algorithm by choosing

?????1??2 and a spatially varying regularization parameter:

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苏州科技学院本科生毕业设计（论文）

??x??where

Q?x? (6) S?x??'?u??v??u Q?x???f?u?di???u?4???,S?x??

???VarxR?Here,? is the standard deviation of image noise,and VarR?x? is the local variance of the residue?f?u?. C. Shock filter

In some special ideas and techniques developed in numerical solutions of nonlinear hyperbolic equations were applied to feature-oriented image enhancement for the first time.Osher and Rudin introduced a novel image sharpening technique,called the shock filter(SF),which is based on a modification of the nonlinear Burgers’ equation,and simulates the shock wave calculation in the computational fluid mechanics.Different from the nonlinear parabolic equation of diffusion-type process,they proposed a hyperbolic one:

?u??sign(uNN)?u (7) ?tWhere sign is a sign function,uNN is the second directional derivative of image along local normal direction to isophote line.It detects an image edge using the zero-crossing of uNN,where a shock is formed at the speed of ?u.

Considering image noise in estimation of edges.Alvarez and Mazorra added a smoothing kernel and coupled the anisotropic diffusion with the shock filter(ADSF) for noise elimination and edge sharpening:

?u??sign?G??uNN??u?cuTT (8) ?twhere G? is a Gaussian kernel with standard deviation ?,uTT is the second directional derivative of image along local tangent direction,and c is a constant to balance the anisotropic diffusion and the shock filter. D. Neighborhood filter

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苏州科技学院本科生毕业设计（论文）

An effective image denoising technique is neighborhood filters,which consider some similarity between two pixels or blocks of image both in spatial location and in gray level.Buades proposed the following nonlocal means(NLM) filter:

?G???u?x?.??u?y?.??2?0??1?u?y?dy (9) exp?? NLhu?x??2????c?x?h???G???u?x?.??u?y?.??2?0???dy is a normalization factor,and where c?x???exp?2????h??????h is a filtering parameter related to noise level.The nonlocal means filter gives better results in denoising textured patterns.

A more complicated neighborhood filter called the Block-Matching and 3D Filtering(BM3D) algorithm was introduced by Dabov et al.which has three main steps:grouping of similar image blocks,3D collaborative filtering of these blocks in the spectrum domain,and aggregation of all local estimates.This algorithm includes a basic estimation and a final estimation using the following weighted average:

w?? u?x????w?RSRSR,SUR,S?x??R,SXs?x?,x?? (10)

where R and S denote the reference block and the similar block respectively, w is the weight of corresponding block, U?x? is the local block-wise estimate,and ??x? is a characteristic function.As they claim,this algoritm is currently one of best denoising methods in terms of peak signal-to-noise ratio.

Finally,as one will see,the total variation regularization methods and the neighborhood filters can only be used for image denoising,while the anisotropic diffusion and the shock filter can be used for both image denoising and enhancement simultaneously,because of their inherent local backward diffusion. Ⅲ. IMPROVED ALGORITHMS

Main information of an image is encoded in its edges,details and textures.These components need to be processed in different ways to enhance the image as well as

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