Many scientific data sets are contaminated by noise, either because of data acquisition process, or because of naturally occurring phenomena. A first step in analyzing such data sets is denoising, i.e., removing additive noise from a noisy image. For images, noise suppression is a delicate and a difficult task. A trade of between noise reduction and the preservation of actual image features has to be made in a way that enhances the relevant image content. The beginning chapter in this thesis is introductory in nature and discusses the Popular denoising techniques in spatial and frequency domains. Wavelet transform has wide applications in image processing especially in denoising of images. Wavelet systems are a set of building blocks that represent a signal in an expansion set involving indices for time and scale. These systems allow the multi-resolution representation of signals. Several well known denoising algorithms exist in wavelet domain which penalize the noisy coefficients by threshold them. We discuss the wavelet transform based denoising of images using bit planes. This approach preserves the edges in an image. The proposed approach relies on the fact that wavelet transform allows the denoising strategy to adapt itself according to directional features of coefficients in respective sub-bands. Further, issues related to low complexity implementation of this algorithm are discussed. The proposed approach has been tested on different sets images under different noise intensities. Studies have shown that this approach provides a significant reduction in normalized mean square error (NMSE). The denoised images are visually pleasing. Many of the image compression techniques still use the redundancy reduction property of the discrete cosine transform (DCT). So, the development of a denoising algorithm in DCT domain has a practical significance. In chapter 3, a DCT based denoising algorithm is presented. In general, the design of filters largely depends on the a-p.