High Dimensional Inference and Signal Recovery

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

This research project is to reconstruct high-dimensional sparse signals based on a small number of measurements, possibly corrupted by noise. More precisely, four of the main objectives of the program are: 1) further weaken the conditions and strengthen the results of current methods. The investigator aims to push the boundary of the field by developing new theoretical tools to analyze the current algorithms; 2) analyze the connections among different methods to get a deeper understanding of the nature of sparse signal recovery problem; 3) extend the research to multichannel setup which involves simultaneously recovery of a set of signals; 4) develop courses for both graduate student and undergraduate student. Build research projects for graduate students. Make the undergraduate students at least be aware of the possible limitation of classical methods and suitable alternatives. Due to advances in science and technology, scientists and engineers are now able to collect and process enormously large data sets of all kinds. Such data sets pose many statistical challenges not encountered in smaller scale studies. One of the key problems in this area is the reconstructing of high-dimensional sparse signals, which is a fundamental problem in signal processing. This and other related problems have attracted much interest in a number of fields including applied mathematics, electrical engineering, statistics, finance, and bioinformatics. The proposed research will benefit applications in these scientific areas, for instance the compression of audio, images, and video signals and the analysis of microarray data. It is also of critical importance in linear regression, signal modeling, and machine learning.