ECE 64100 Model-Based Image and Signal Processing

Course Description: ECE 64100 Model-Based Image and Signal Processing

Textbook: Model Based Imaging Notes: course notes

Labs: instruction

• maximum a posteriori (MAP) image restoration The lab explores the use of maximum a posteriori (MAP) estimation of images from noisy and blurred data using both Gaussian Markov random field (GGMRF) and non-Gaussian Markov random field (MRF) prior models (Generalized Gaussian MRF (GGMRF) and q-Generalized GMRF(QGGMRF)). We solved the high dimensional optimization problem of MAP estimation with iterative coordinate descent (ICD) techniques.
• expectation-maximization (EM) algorithm, API docs for source code This lab explores the use of the expectation-maximization (EM) algorithm for the estimate of parameters. In particular, we will use the EM algorithm to estimate the parameters of Gaussian mixture distribution, and implement the method for automaticaly determining the number of clusters in a Gaussian mixture model by minimizing the minimum description length (MDL) estimator.

Homeworks:

• probability, Gaussian random variables
• MAP, ML and MMSE Estimators, conditional distribution of Gaussian, time-reversibility of Gaussian processes
• Gaussian autoregressive (AR) models

Topics:

• Alternating Direction Method of Multipliers (ADMM), paper, slides
• MCMC - CMU slides,

Blogs:

• an ADMM based framework for AutoML pipeline configuration, blog
• applications of ADMM, ADMM explanation, introduction to ADMM
• optimization techniques
• L1, L2 regularizations and Laplace, Gaussian priors
• MCMC: Metropolis Hastings, Hamiltonian Monte Carlo, MCMC explanation, MCMC. MCMC methods

References:

• Convex Optimization: CMU Fall 2019