【正文】 s MRI images. The scope of the paper is to focus on noise removal techniques for natural images. 2. Evolution of Image Denoising Research Image Denoising has remained a fundamental problem in the field of image processing. Wavelets give a superior performance in image denoising due to properties such as sparsest and mulltire solution structure. With Wavelet Transform gaining popularity in the last two decades various algorithms for denoising in wavelet domain were introduced. The focus was shifted from the Spatial and Fourier domain to the Wavelet transform domain. Ever since Donoho’s Wavelet based threshold approach was published in 1995, there was a surge in the denoising papers being published. Although Donoho’s concept was not revolutionary, his methods did not require tracking or correlation of the wavelet maxima and minima across the different scales as proposed by Mallat. Thus, there was a renewed interest in wavelet based denoising techniques since Donoho demonstrated a simple approach to a difficult problem. Researchers published different ways to pute the parameters for the threshold of wavelet coefficients. Data adaptive thresholds were introduced to achieve optimum value of threshold. Later efforts found that substantial improvements in perceptual quality could be obtained by translation invariant methods based on threshold of an Undecimated Wavelet Transform. These threshold techniques were applied to the nonorthogonal wavelet coefficients to reduce artifacts. Multiwavelets were also used to achieve similar results. Probabilistic models using the statistical properties of the wavelet coefficient seemed to outperform the thresholding techniques and gained ground. Recently, much effort has been devoted to Bayesian denoising in Wavelet domain. Hidden Markov Models and Gaussian Scale Mixtures have also bee popular and more research continues to be published. Tree Structures ordering the wavelet coefficients based on their magnitude, scale and spatial location have been researched. Data adaptive transforms such as Independent Component Analysis (ICA) have been explored for sparse shrinkage. The trend continues to focus on using different statistical models to model the statistical properties of the wavelet coefficients and its neighbors. Future trend will be towards finding more accurate probabilistic models for the distribution of nonorthogonal wavelet coefficients. 3. Classification of Denoising Algorithms As shown in Figure 1, there are two basic approaches to image denoising, spatial filtering methods and transform domain filtering methods. Spatial Filtering A traditional way to remove noise from image data is to employ spatial filters. Spatial filters can be further classified into nonlinear and linear filters. I. NonLinear Filters With nonlinear filters, the noise is removed without any attempts to explicitly identify it. Spatial filters employ a low pass filtering on groups of pixels with the assumption that the noise occupies the higher region of frequency spectrum. Generally spatial filters remove noise to a reasonable extent but at the cost of blurring images which in turn makes the edges in pictures invisible. In recent years, a variety of nonlinear median type filters such as weighted median, rank conditioned rank selection, and relaxed median have been developed to overe this drawback. II. Linear Filters A mean filter is the optimal linear filter for Gaussian noise in the sense of mean square error. Linear filters too tend to blur sharp edges, destroy lines and other fine image details, and perform poorly in the presence of signaldependent noise. The wiener filtering method requires the information about the spectra of the noise and the original signal and it works well only if the underlying signal is smooth. Wiener method implements spatial smoothing and its model plexity control correspond to choosing the window size. To overe the weakness of the Wiener filtering, Donoho and Johnstone proposed the wavelet based denoising scheme in. Transform Domain Filtering The transform domain filtering methods can be subdivided according to the choice of the basis functions. The basis functions can be further classified as data adaptive and nonadaptive. Nonadaptive transforms are discussed first since they are more popular. SpatialFrequency Filtering Spatialfrequency filtering refers use of low pass filters using Fast Fourier Transform (FFT). In frequency smoothing methods the removal of the noise is achieved by designing a frequency domain filter and adapting a cutoff frequency when the noise ponents are decorrelated from the useful signal in the frequency domain. These methods are time consuming and depend on the cutoff frequency and the filter function behavior. Furthermore, they may produce artificial frequencies in the processed image. Wavelet domain Filtering operations in the wavelet domain can be subdivided into linear and nonlinear methods. I. Linear Filters Linear filters such as Wiener filter in the wavelet domain yield optimal results when the signal corruption can be modeled as a Gaussian process and the accuracy criterion is the mean square error (MSE). However, designing a fi