This research focuses on estimation and signal processing for spatial data. Three major areas are considered. The first deals with efficient algorithms for the processing of spatial data. Problems to be addressed include (i) the employment of novel notions of recursion as well as spatial decompositions to develop recursive and highly parallel algorithms for the estimation of 2-D processes described by noncausal models and for other 2-D digital filtering applications; and (ii) the exploitation of the symmetries present in some classes of random fields (e.g. isotropic fields) to develop efficient procedures for recursive and spectral estimation. The second deals with the development of algorithms for inverse and signal reconstruction problems in several dimensions. Among the problems to be investigated are (i) the development of efficient and generalized-tomographic methods for exact and approximate solution of 2-D and 3-D inverse scattering problems; and (ii) the development of system- identification-based approaches to inverse problems with particular emphasis on algorithms that work at multiple spatial scales. The third area deals with computational vision and geometry. A number of research problems are described including (i) the development of estimation-based algorithms for problems of computational vision such as motion and depth estimation; and (ii) the investigation of system and estimation-theoretic formulations of problems in computational geometry such as the reconstruction of objects given uncertain measurements of various quantities such as the support of a convex object, its silhouette, its interior, etc. This research focuses on estimation and signal processing for spatial data. The three major areas considered are (i) efficient algorithms for the processing of spatial data (ii) the development of algorithms for inverse and signal reconstruction problems in two and three dimensions and (iii) questions related to computational vision and geometry.
