Bayesian Reimaging of Sparsity in Inverse Problems - SIAM-IS Virtual Seminar
Society for Industrial and Applied Mathematics via YouTube
Overview
Syllabus
Intro
Linear Sparse Inverse Problems
Sparsity as a Belief
Sparsity in a Bayesian Way
Sparsity promoting priors
Hierarchical prior model for sparsity
The Bayesian solution is the posterior
Iterated Alternating Sequential (IAS) algorithm
IAS algorithm for Generalized Gamma hyperpriors
Approximate IAS and reduced model: the x update
The Gamma hyperprior (r = 1)
From Gamma to Generalized Gamma hyperprior
Convexity region
Special Generalized Gamma hyperpriors
Global Hybrid IAS
Support of the signal the meaning of
Computed example: 1D test
Computed examples: starry night
Dictionary Learning
MNIST Data: Handwritten digits
MNIST Dataset example: mismatch noise 0.01
MNIST Dataset: mismatch noise 0.05
Taught by
Society for Industrial and Applied Mathematics