| Image restoration represents one of the primary focal points of research in digital image processing. Since the 1960's, engineers have spent considerable effort to develop efficient and effective algorithms to restore degraded images. Because of this, the field is rich with mathematical concepts and algorithms which are especially suited to solve this inverse problem. One avenue which has not received substantial attention up to this point, however, is the application of multiresolution concepts to the image restoration problem. This thesis, therefore, develops a general framework for image restoration in a multiresolution environment based on the wavelet transform. Classical approaches to image restoration including direct, iterative and recursive methods, normally implemented in both the discrete frequency and spatial domains, are cast into a multiresolution framework here. The resulting contributions of this work include a unique approach to nonstationary image restoration using a new multichannel matrix formulation of a wavelet-based subband decomposition, and a novel adaptive approach to the restoration of degraded images using multiscale stochastic modeling of noisy-blurred wavelet detail coefficients. A wavelet domain analysis of the behavior of the linear blurring operators associated with the image degradation problem is presented, and the effects of the cross-channel and cross-scale blur terms are carefully considered in each of the algorithms developed.; The new techniques presented here show a marked improvement, both by objective and subjective quality measures, over their classical counterparts. The improvements are especially evident in the multichannel Wiener filter, developed here for wavelet-based data, when accurate estimates of auto and cross-subband correlations are available. In addition, very noticeable perceptual improvements are also obtained with the multiscale quadtree coefficient filtering framework addressed in this thesis. Adaptive noise smoothing and restoration algorithms applied to quadtree structures of wavelet detail coefficients possess a very efficient way to include adaptivity to the local spatial activity in an image. Each restoration technique developed here takes advantage of the edge-like properties of the wavelet transform, and it is largely this aspect of wavelet-based algorithms that gives rise to more perceptually pleasing results than those of most classical image restoration approaches. |
