图像的小波降噪

时间：2023-03-07 08:18:32 数学毕业论文我要投稿

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图像的小波降噪

摘要：图像降噪1直是图像处理领域1个研究得比较多的课题，也是1个热点领域。其中小波变换降噪技术是被研究的最多1种技术，本文主要讨论近几年兴起的阈值降噪技术。2维小波分析用于图像降噪的步骤如下。
（1）2维图像信号的小波分解。在这1步，应当选择合适的小波和恰当的分解层次（记为N），然后对待分析的2维图像信号进行N层分解计算。
（2）对分解后的高频系数进行阈值量化。对于分解的每1层，选择1个恰当的阈值，并对该层高频系数进行软阈值量化处理。
（3）2维图像信号的小波重构。同样的，根据小波分解后的第N层的近似（低频系数）和经过阈值量化处理后的各层细节（高频系数），来计算2维信号的小波重构。
还介绍了小波的数学基础。如：小波变换，小波离散及框架，多分辨率分析和Mallat算法的信号分解和重建过程。
图像信号的小波降噪步骤和1维信号的降噪步骤完全相同，所不同的是，处理工具是用2维小波分析工具代替了1维小波分析工具。利用MATLAB 7 ，通过具体的例子来说明如何利用小波分析进行图像降噪这个问题。
关键字：图像降噪；小波分解；阈值量化；小波重构

Denoising Image by Using Wavelet

Abstract：Image noise reduction has been an area of image processing more research topics, as well as a hot field. Wavelet transform noise suppression technology is a study of the most technical, In this paper, we mainly discusses the noise suppression technology of noise threshold which is a method rising in recent years. Wavelet analysis for the two-dimensional image noise reduction steps are as follows.
(1) The wavelet decomposition of two-dimensional image. In this step, we should choose a suitable and appropriate wavelet decomposition levels (recorded as N), then decompose the 2-D analyzed image signal into N layer decomposition.
(2) Threshold Quantified about the high-frequency coefficients decomposed. For each level of decomposition, we choice an appropriate threshold, and decide the quantity of the soft threshold for high-frequency coefficients of this layer.
(3) The reconstruction of two-dimensional image signal by using wavelet. Similarly, according to the approximation of the Nth level (coefficient of low frequency) decomposed by using wavelet and the various details (coefficient of high-frequency) after quantified for the threshold values, calculate the wavelet reconstruction for the two-dimensional signal.
The mathematical base of wavelet also is introduced, such as: wavelet’s transformation, discrete wavelet and framework, multi-resolution analysis, Mallat algorithm for the process of decomposition and reconstruction of a signal.
The steps of noise reduction by using wavelet for image signal are identical to the steps of one-dimensional signal noise reduction. The only difference is the process tools. It is using two-dimensional wavelet analysis tools instead of one-dimensional wavelet analysis tools. By using MATLAB 7, through specific examples illustrate how to use wavelet analysis to denoise for an image.
Keywords： image noise reduction ( denoise of a image); decomposition applying wavelet; quantization of a threshold、reconstruction by using wavelet

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