14 research outputs found
Fractal Image Coding as Projections Onto Convex Sets
Abstract. We show how fractal image coding can be viewed and gen-eralized in terms of the method of projections onto convex sets (POCS). In this approach, the fractal code denes a set of spatial domain sim-ilarity constraints. We also show how such a reformulation in terms of POCS allows additional contraints to be imposed during fractal image decoding. Two applications are presented: image construction with an incomplete fractal code and image denoising.
Incremental proximal methods for large scale convex optimization
Laboratory for Information and Decision Systems Report LIDS-P-2847We consider the minimization of a sum∑m [over]i=1 fi (x) consisting of a large
number of convex component functions fi . For this problem, incremental methods
consisting of gradient or subgradient iterations applied to single components have
proved very effective. We propose new incremental methods, consisting of proximal
iterations applied to single components, as well as combinations of gradient, subgradient,
and proximal iterations. We provide a convergence and rate of convergence
analysis of a variety of such methods, including some that involve randomization in
the selection of components.We also discuss applications in a few contexts, including
signal processing and inference/machine learning.United States. Air Force Office of Scientific Research (grant FA9550-10-1-0412