Novel algorithms for learning overcomplete dictionaries

Using a Bayesian framework based on an assumption of a convex/Schur-convex (CSC) log-prior, together with an associated affine-scaling transformation (AST) optimization algorithm, a signal vector, y, can be succinctly represented within a very overcomplete m/spl times/n dictionary of representation vectors a/sub i/, A=[a/sub 1/,...,a/sub n/], n/spl Gt/m, dictionary by obtaining a sparse solution, x, to the linear inverse problem Ax/spl ap/y/spl dot/. In this paper we outline how novel approximate maximum likelihood (AML) and maximum a posteriori (MAP) over-complete dictionary learning algorithms can be developed within the CSC/AST framework.