Denoising and compression of digital images using wavelets

This thesis concentrates primarily on two problems that concern noise corrupted images and looks to the wavelet domain for the solutions. Firstly, the issue of noise reduction in digital images is addressed. Most of the popular thresholding techniques are either subband adaptive, i.e., do not adapt spatially according to individual subband coefficients, or rely heavily on subband statistics for adaptation, which makes them computationally expensive. A low-complexity adaptation of the subband-optimal thresholds according to the individual coefficients is presented. The correlation that exists in consecutive subbands in wavelet domain is exploited to adapt the subband optimal thresholds using the magnitude of the corresponding parent coefficients. Using simulated experiments, the ability of the proposed algorithm to preserve the edges and fine details in an image, while successfully reducing the noise from the smooth regions, is demonstrated. Secondly, the relatively uncharted area of simultaneous denoising and compression of images that are corrupted with noise is explored. A data adaptive subband (wavelet) coder that performs joint denoising and compression of the input image based on both the additive white Gaussian noise level in the image and the compression rate desired is developed. A simple uniform threshold quantizer (UTQ), with centroid reconstruction, is adapted to have a joint noise level (data) and output bitrate adaptive zero-zone and reconstruction. To improve the performance of this variable-rate-coder, a context-based classification scheme that improves the quantization of the fine detail in the image is also proposed. The joint denoising and compression scheme is further extended for the removal of multiplicative speckle from medical Ultrasound images using homomorphic filtering