圖像的小波降噪

圖像的小波降噪
 

摘要：圖像降噪1直是圖像處理領域1個研究得比較多的課題，也是1個熱點領域。其中小波變換降噪技術是被研究的最多1種技術，本文主要討論近幾年興起的閾值降噪技術。2維小波分析用于圖像降噪的步驟如下。
   （1）2維圖像信號的小波分解。在這1步，應當選擇合適的小波和恰當的分解層次（記為N），然后對待分析的2維圖像信號進行N層分解計算。
（2）對分解后的高頻系數進行閾值量化。對于分解的每1層，選擇1個恰當的閾值，并對該層高頻系數進行軟閾值量化處理。
（3）2維圖像信號的小波重構。同樣的，根據小波分解后的第N層的近似（低頻系數）和經過閾值量化處理后的各層細節(jié)（高頻系數），來計算2維信號的小波重構。
還介紹了小波的數學基礎。如：小波變換，小波離散及框架，多分辨率分析和Mallat算法的信號分解和重建過程。
圖像信號的小波降噪步驟和1維信號的降噪步驟完全相同，所不同的是，處理工具是用2維小波分析工具代替了1維小波分析工具。利用MATLAB 7 ，通過具體的例子來說明如何利用小波分析進行圖像降噪這個問題。
   關鍵字：圖像降噪；小波分解；閾值量化；小波重構

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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