Both wavelet denoising and denoising methods using the concept of sparsity are based on softthresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the Fourier, DCT, and/or wavelet domain. The transfer domain coefficients of the noisy signal are projected onto `1-balls to reduce noise. In this lecture note, we establi...

...................................................................................................................... ii Co-Authorship ........................................................................................................... iv Epigraph ................................................................................................................... vii Dedication .............

The dissertation of Alden King is approved, and it is acceptable in quality and form for publication on microfilm and electronically: 2012 iii DEDICATION To myself, fifty years from now. May this be the least of your accomplishments. iv EPIGRAPH The Jews were amazed and asked, " How did this man get such learning without having studied? "

We consider a nite or in nite family of closed convex sets with nonempty intersection in a normed space A property relating their epigraphs with their intersection s epigraph is studied and its relations to other constraint quali cations such as the linear regularity the strong CHIP and Jameson s G property are estab lished With suitable continuity assumption we show how this property can be en...

2.1. Computation of the hypograph of a tree along one of the dimensions of the modeling space 134 2.2. Tree traversal with regeneration of minimal nodes along the generation direction ..... 135 2.3. Computation of the epigraph of a tree along one of the directions of the modeling space 137 2.4. Tree traversal with regeneration of maximal nodes along the generation

2010 iii DEDICATION To Christina, whose love and support made this possible. iv EPIGRAPH In a few minutes a computer can make a mistake so great that it would have taken many men many months to equal it. –Anonymous With the GPU, this may be possible in just a few seconds. –Fred

This work aims at partially bridging the gap between (generic but slow) “generalpurpose” convex solvers and (fast but constricted) “specialized” solvers. We develop the Epsilon system, a solver capable of handling general convex problems (inputs are specified directly as disciplined convex programs); however, instead of transforming these problems to cone form, the compiler transforms them to a...