Redundant directional wavelet transforms for image processing

This thesis introduces two algorithms for image denoising and a technique for image enhancement and edge detection. The two new denoising schemes namely Directional Slice Wavelet Transform (DSWT) and the Sliced Ridgelet Transform (SRT), are based on redundant directional wavelet transforms. These approaches provide superior denoising results than contemporary denoising techniques like wavelet and curvelet transforms, and offers comparable performance to the Wavelet based Hidden Markov Tree (WHMT) method.; The DSWT uses the one-dimensional wavelet transform computed along several directions on the image. Inspired from ridgelets and curvelets, the DSWT method explores redundancy of the wavelet transform and its property to easily detect singularities to remove noise without smearing the edges in the image.; The second approach for denoising called the SRT is an extension of the DSWT and is originated from the concepts of ridgelets. The SRT method gives superior results to wavelet, ridgelet and curvelet transforms, and provides comparable results to the DSWT and WHMT techniques. (Abstract shortened by UMI.)...