Edge -preserving models and efficient algorithms for ill-posed inverse problems in image processing

Suhail S Saquib, Purdue University

Abstract

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 effective means of estimating the large number of model parameters. We have tackled this problem in the multiresolution framework, where the space-varying model parameters at any resolution are estimated from the coarser resolution image. Experimental results on real tomographic data sets and optical flow estimation results on real image sequences demonstrate that the multiresolution non-homogeneous model results in cleaner and sharper images as compared to the fixed resolution homogeneous model. Moreover, the superior quality is achieved at no additional computational cost. The last part of this research deals with efficient image reconstruction from time-resolved diffusion data, which employs a finite-difference approach to solve the diffusion equation and adjoint differentiation to compute the gradient of the cost criterion. The intended application is medical optical tomography.

Degree

Ph.D.

Advisors

Bouman, Purdue University.

Subject Area

Electrical engineering

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