ESE 559 - Digital Image Processing II (Bayesian Image Processing)

Course Syllabus

I. Introduction

What is Image Processing? Why a Probabilistic Approach?

II. Mathematical Background

Notation and Math Conventions. Topics in Linear Algebra. Fourier Theory. Stochastic Background including basic probability, random variables and random fields.

III. Introduction to Estimation Theory

Intro to Decision Theory. Maximum Likelihood Estimation. MAP estimation. MMSE estimates.

IV. Deterministic Aspects of the Imaging Model

Concept of system matrix, Null functions, Unified description in terms of SVD

V. Image Formation- The Image Likelihood

Physics of image formation as a likelihood function. The Poisson model. The Gaussian model. Other models.

VI. Bayesian Models for Image Processing

Types and roles of prior knowledge, including spline models for smoothing. Case study of Gaussian likelihood with smoothing stabilizer. Case study- tomography

VII.Markov Random Fields

Motivation for MRF's -role of spatial discontinuities. Basic of MRF theory. Gibbs priors for restoration.

VIII. Applications of MRF Models

Restoration/reconstruction. Segmentation.

IX. Markov Chain Monte Carlo

Hastings algorithms, Gibbs sampler, Simulated Annealing. Applications.

X. Mixture Models for Segmentation

Mixture models, EM algorithm, application to image segmentation