Digital Signal Processing

Contains reports on twelve research projects.U. S. Navy - Office of Naval Research (Contract N00014-75-C-0951)National Science Foundation (Grant ENG76-24117)National Aeronautics and Space Administration (Grant NSG-5157)Joint Services Electronics Program (Contract DAABO7-76-C-1400)U.S. Navy-Office of Naval Research (Contract N00014-77-C-0196)Woods Hole Oceanographic InstitutionU. S. Navy - Office of Naval Research (Contract N00014-75-C-0852)Department of Ocean Engineering, M.I.T.National Science Foundation subcontract to Grant GX 41962 to Woods Hole Oceanographic Institutio

Radio Astronomy

Contains reports on sixteen research projects.National Science Foundation (Grant AST81-21416)National Science Foundation (Grant AST80-22864)National Aeronautics and Space Administration (Contract S-10665-C)National Aeronautics and Space Administration (Contract NAGW373)National Science Foundation (Grant AST79-19553)National Oceanic and Atmospheric Administration (Grant 04-8-M01-1)National Aeronautics and Space Administration (Grant NAG5-10)National Aeronautics and Space Administration (Contract NAS5-22929)Defense Advanced Research Projects Agency (Contract MDA 903-82-K-0521)Intelsat (Contract Intel-188)Joint Services Electronics Program (Contract DAAG29-80-C-0104)Lockheed Missiles and Space Company (Contract LS90B4860F

Radio Astronomy

Contains summary of research and reports on nine research projects.National Science Foundation (Grant AST81-21416)National Science Foundation (Grant AST82-14296)National Aeronautics and Space Administration (Grant S-10781-C)National Aeronautics and Space Administration (Grant NAGW-373)National Science Foundation (Grant AST79-19553)M.I.T. Sloan Fund for Basic ResearchNational Oceanic and Atmospheric Administration (Grant 04-8-M01-1)National Aeronautics and Space Administration (Grant NAG5-10)National Aeronautics and Space Administration (Contract NAS5-22929)Defense Advanced Research Projects Agency (Contract MDA 903-82-K-0521)Center for Advanced Television Studie

The Convex Geometry of Linear Inverse Problems

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include well-studied cases such as sparse vectors and low-rank matrices, as well as several others including sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures. The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm. The facial structure of the atomic norm ball carries a number of favorable properties that are useful for recovering simple models, and an analysis of the underlying convex geometry provides sharp estimates of the number of generic measurements required for exact and robust recovery of models from partial information. These estimates are based on computing the Gaussian widths of tangent cones to the atomic norm ball. When the atomic set has algebraic structure the resulting optimization problems can be solved or approximated via semidefinite programming. The quality of these approximations affects the number of measurements required for recovery. Thus this work extends the catalog of simple models that can be recovered from limited linear information via tractable convex programming

Elsevier

Multiresolution stochastic models, data fusion, and wavelet transforms