影象的小波降噪
摘要：影象降噪1直是影象處理領域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維小波分析用於影象降噪的步驟如下。
（1）2維影象訊號的小波分解。在這1步，應當選擇合適的小波和恰當的分解層次（記為N），然後對待分析的2維影象訊號進行N層分解計算。
（2）對分解後的高頻係數進行閾值量化。對於分解的每1層，選擇1個恰當的閾值，並對該層高頻係數進行軟閾值量化處理。
（3）2維影象訊號的小波重構。同樣的.，根據小波分解後的第N層的近似（低頻係數）和經過閾值量化處理後的各層細節（高頻係數），來計算2維訊號的小波重構。
還介紹了小波的數學基礎。如：小波變換，小波離散及框架，多解析度分析和Mallat演算法的訊號分解和重建過程。
影象訊號的小波降噪步驟和1維訊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影象降噪這個問題。
關鍵字：影象降噪；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