Wavelet-based Image and Video Processing

Since the last decade the study of the wavelet transform has attracted many efforts and made great progresses. However, the research interest is still growing. In this thesis, we investigate the applications of the wavelet transform to image and video processing. We first study the wavelet transform mainly from a statistical point of view. Specifically, we study the statistics of the wavelet coefficients of 1-D and 2-D Gaussian autoregressive processes, since these models are widely-used in signal and image processing. We found the covariance matrices of the wavelet coefficients are quite sparse with significant correlations concentrating in the interand intra-scale neighborhood. We thus propose to perform the strip Kalman filtering in the wavelet domain (instead of in the spatial domain) and propose a procedure to find optimal strips under complexity constraints. Experimentally, we showed that the structure of the wavelet-based strip Kalman filter is not sensitive to noise strength and achieved much better or comparable error variances than its spatial counterpart. We then proceed to use the wavelet transform for natural image denoising. It is well known the current wavelet-based image denoising approaches suffers from Gibbs-like denoising artifacts. We found this problem is mainly due to neglecting strong correlations of wavelet coefficients, especially in the edge areas. We thus propose to remove edges (statistical means) prior to performing the wavelet transform. This is achieved through a clustering-based nonlinear weighting processing. Another wavelet-based image processing we studied is the multiresolution image enhancement. In the wavelet domain, the image enhancement problem can be treated as estimating the (lost) high-frequency wavelet coefficients from the low-frequency ones. We