Wavelet Transform Based Image Denoising

Abstract

Image denoising has always been one of the standard problems of the image analysis and processing community. It is motivated by itself or by some practical application such as preprocessing for e.g. remote sensing applications, medical image diagnosis; the goal is to reduce noise. The successful image denoising algorithms are mainly based on transforms. Recent research in transform based image denoising has stressed on the wavelet transform due to its superior performance over other transforms such as Fourier, Karhunen-Loeve transform, discrete cosine transform. It is applied to image processing successfully. It has been shown in several papers that wavelet-based methods arise naturally for image denoising. The proposed algorithms for additive noise use local adaptivity based on static of neighboring pixels in wavelet domain. It consists of energy and variance in different scales that capture regularities of natural images. The existing methods have following assumptions:1. The wavelet coefficients are independent; 2. The signal component of the wavelet coefficient distribution follows a specified parametric model. 3. The representation of wavelet of all signal has same level of sparsity. The proposed two methods based on local adaptivity are locally adaptive energy(LAE) and locally adaptive variance(LAV). The algorithm uses Discrete Wavelet Transform(DWT) to extract information about sharp images in multiresoultion images and applies shrinkage function adapting the local statistics of the image. The algorithm use very few and intuitive parameter. The cost function used for the optimization process is to minimize the mean square error. A very important aspect of all the denoising methods and proposed methods is to the accurate estimation of the noise level. Two methods are implemented and assessed thoroughly, one in spatial domain and other in wavelet. The multiplicative noise is reduced to detect geographical features in synthetic aperture radar(SAR). SAR images are corrupted by speckle noise. Existence of this noise may hide details and thus, reduce resolution of these images. The speckle degrades the quality of the image and makes difficult to interpret, analysis and classification of the SAR images. Speckle is reduced by multiscale analysis in wavelet domain The image can be enhanced by using image regularity. Enhancement often includes a denoising and a deblurring or sharpening step. It has been shown that the Holder regularity is decreased with additive white Gaussian noise. The regularity is estimated by wavelet coefficient in different scale then it is increased as perceived by a human observer.