Edge-preserving Models and Efficient Algorithms for Ill-posed Inverse Problems in Image Processing

Saquib, Suhail S. Ph. D., Purdue University, May 1997. Edge-Preserving Models and Efficient Algorithms for Ill-Posed Inverse Problems in Image Processing. Major Professor: Charles A. Bouman. The goal of this research is to develop detail and edge-preserving image models to characterize natural images. Using these image models, we have developed efficient unsupervised algorithms for solving ill-posed inverse problems in image processing applications. The first part of this research deals with parameter estimation of fixed resolution Markov random field (MRF) models. This is an important problem since without a method to estimate the model parameters in an unsupervised fashion, one has to reconstruct the unknown image for several values of the model parameters and then visually choose between the results. We have shown that for a broad selection of MRF models and problem settings, it is possible to estimate the model parameters directly from the data using the EM algorithm. We have proposed a fast simulation technique and an extrapolation method to compute the estimates in a few iterations. Experimental results indicate that these fast algorithms substantially reduce computation and result in good parameter estimates for real tomographic data sets. The second part of this research deals with formulating a functional substitution approach for efficient computation of the MAP estimate for emission and transmission tomography. The new method retains the fast convergence of a recently proposed Newton-Raphson method and is globally convergent. The third part of this research deals with formulating non-homogeneous models. Non-homogeneous models have been largely ignored in the past since there was no