Image Processing with Multiscale Stochastic

In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a two-sweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illustrate how the multiscale models can be used in the context of regularizing ill-posed inverse problems and demonstrate the substantial computational savings that such an approach ooers. Several novel features of the approach are developed including a technique for choosing the optimal resolution at which to recover the object of interest. Next, we show that this class of models contains other widely used classes of statistical models including 1-D Markov processes and 2-D Markov random elds, and we propose a class of multi-scale models for approximately representing Gaussian Markov random elds. These results, coupled with those illustrating the computational eeciencies that the multi-scale models lead to, suggest that the multiscale framework is a powerful paradigm for image processing both because of the eecient algorithms it admits and because of the rich class of phenomena it can be used to describe. This motivates us in the nal section of this thesis to pursue further algorithmic development for the multi-scale models. In particular, we develop an eecient likelihood calculation algorithm for multiscale models and demonstrate an application of the algorithm in the area of texture discrimination. The thesis concludes with a review of our main results and with a discussion of a few of the many open problems and promising directions for further research and application. Acknowledgments I want to thank my thesis advisor, Alan Willsky, for the input and guidance he gave to me throughout my doctoral program at MIT. His perspective and insight has had a profound innuence both on this thesis and on my professional development. I also wish to thank the members of my thesis committee, and Greg Wornell. They all provided important criticism and invaluable comments. Clem Karl, in particular, provided substantial input throughout the period during which this research was being done. Thanks are also in order for Albert Benveniste, Claude Labit, Fabrice Heitz and Patrick Bouthemy for their hospitality and help during my visit to France in the summer of 1991. I want to thank my ooce-mates and friends at MIT, past and present, who in …