Alan S. Willsky - US grants

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.

This award will support collaborative research in electrical engineering and computer science between two US and French groups. The US researchers are: Drs. Allan Willsky and Sanjoy Mitter, Massachusetts Institute of Technology, and Dr. Bernard Levy, University of California at Davis. The French researchers are: Drs. A. Benveniste, R. Nikoukhah and M. Basseville, French National Institute for Computer Science and Automation (INRIA). The research will focus on five topics: 1) multi-resolution statistical signal and image processing, including the development of novel multi-scale stochastic models for efficient and highly parallel algorithms 2) discrete event systems, including the blending of concepts from computer science and control in order to develop an effective methodology for the monitoring and control of complex systems 3) noncausal system models and efficient parallel algorithms for optimal estimation 4) distributed parameter systems, including a complete treatment of infinite dimensional systems and 5) system and estimation-theoretic approaches to computer vision. The project will benefit from the history of previous and successful collaboration between these two groups and the extensive and complementary expertise of the US and French investigators.

Willsky There are three major components of this research program which has as its overall objective the development of new classes of algorithms for statistical signal processing and estimation of spatial and multidimensional data. The first is the development of statistical models and methods for multiscale signal analysis and processing in one and several dimensions. Problems that are being addressed include the development of a statistical counterpart to the emerging theory of multiresolution signal decompositions and wavelet transforms, the investigation of iterative, multigrid signal processing algorithms, and applications of these methods to topics ranging from inverse reconstruction problems to problems of signal or image segmentation. The second is the development of efficient algorithms for processing spatial data. This topic focuses on the exploitation of the structure of noncausal models, such as those described by partial difference equations or Markov random fields, in order to develop extremely efficient and highly parallel algorithms. Specific problems being investigated include the employment of radially inward and outward recursions for multidimensional signal processing, parallel processing structures based on spatial partitioning of multidimensional signal processing, and the development of efficient algorithms for tracking motion and other temporal changes in space-time random fields. The third is the development of statistical methods for estimating or reconstructing geometric features in multidimensional data given uncertain measurements of various quantities, such as the support of a convex object in 2-D or 3-D, or the 2-D silhouette of 3-D objects.

9316624 Willsky A new prognostic model of the global ocean circulation is being developed based on the Navier-Stokes equations, using state-of-the-art parallel computers and languages with an ultimate goal of creating a global ocean modeling/estimation tool that can be used for climate research. A key element of this endeavor is the development of statistical estimation algorithms for the assimilation of data into the forward model. The combined forward/estimation model could be used to estimate the state of the ocean form observations constrained by dynamics. The data of concern is sparse, heterogeneous and multiresolution and the associated global ocean circulation models are of gargantuan size, having upwards of 10 ~ 10 degrees of freedom. The resulting estimation problem is of such a large size that standard computational procedures become prohibitive. Novel approaches to statistical modeling and the circulation models are needed. We proposed the first steps in this direction through the establishment of a collaboration involving physical oceanographers and probabilistic modeling and statistical inference specialists. The short term focal point of this collaboration is the definition and solution of a series of subproblems designed to foster understanding insight, and mutual communication and in the process advance the state of the art in both data assimilation for global ocean modeling and statistical modeling and estimation of random fields. ***

9313898 Willsky This three-year awards supports ongoing U.S.-France cooperative research in image and signal processing among investigators from the Massachusetts Institute of Technology, the University of California at Davis, and INRIA/Rocquencourt and Rennes (French National Institute for Research in Computer Science and Applied Mathematics). The U.S. and French teams are led by Alan Willsky, MIT, and Albert Benveniste, INRIA. The objective of their research is to investigate various problems in geometric modeling, nonlinear systems, and image processing. They will study (1) multiresolution statistical signal and image processing; (2) failure and event detection; (3) new approaches to nonlinear parameter systems; and (4) discrete event systems. The U.S. and French investigators have considerable expertise on all these topics. The project takes advantage in particular of substantial French advances in nonlinear systems modeling and different, but complementary, approaches to problems in discrete event systems. The French are also considered world experts in systems described by partial differential equations. The collaboration will advance understanding on analysis and design of circuits for signal processing applications. ***

ITR/AP: An Ensemble Approach to Data Assimilation in the Earth Sciences

New data sources are beginning to have a dramatic impact on our ability to understand the earth as an integrated system. Our prospects for dealing with the environmental issues of the 21st century -- climate change, population pressures on natural resources, and major modifications in global element cycles -- depend largely on this new information. However, our ability to process and interpret environmental data is not keeping pace with the dramatic increase in available information, especially information from airborne and orbital remote sensing platforms. If we are to realize the potential benefits of new sensing technologies we will need to develop intelligent environmental data assimilation procedures that are able to efficiently extract useful information about the earth from a diverse set of data sources.

Environmental data assimilation can be posed as a problem of estimating a large number of unobservable or highly uncertain variables (e.g. sea surface heights, atmospheric pressures, hydrologic fluxes, etc.) from a large number of related but noisy measurements (e.g. microwave radiances or backscatter detected by a satellite sensor). The estimation procedure relies on mathematical models that relate unknowns to measurements. Environmental estimation problems are challenging because the systems of interest: 1) are spatially distributed and highly variable over a wide range of space and time scales, 2) are difficult to describe with precision, 3) are often nonlinear, even chaotic, and 4) are often characterized by non-unique relationships between unknowns and measurements.

This project is concerned with very large problems (many measurements and many unknowns) which are not amenable to traditional data assimilation techniques but are of crucial interest to researchers in the earth sciences. An interdisciplinary team will develop a better understanding of the issues of dimensionality reduction and uncertainty propagation that are crucial to large-scale data assimilation. So-called ensemble methods provide a particularly informative way to identify these key features. A new generation of "intelligent" data assimilation methods will be developed that build on the understanding gained from the reduced problem. The applicability of these methods will be investigated on problems of broad interest in the earth sciences, including problems that 1) deal with coupled systems, 2) cut across traditional disciplines, and 3) work with remote sensing data sets.

This ITR project brings together acknowledged experts on environmental data assimilation. It is a group ITR project, rather than several individual projects, which cuts across earth science disciplines. The research will be coordinated with: 1) a seminar series, 2) joint supervision of Ph.D. students and post-doctoral researchers, 3) a Ph.D. mentoring program, 4) a selection of cross-cutting sample problems, and 5) co-authored publications.