MSPA-MCS: High-Dimensional, Nonparametric Density Estimation for the Analysis of Images and Shapes

University Of Utah, Salt Lake City UT

Investigators

Abstract

A proliferation of technical instruments, computational resources, and digital media are opening up new opportunities in security, entertainment, science and medicine. We are automatically acquiring large databases of measurements that span physical scales from the molecule, to the cell, tissue, organism, ecosystem, and beyond to stars and galaxies. However, the rate of acquisition of these data exceeds our ability to analyze them, and many applications are stymied not by the lack of data but by the daunting task of understanding it all. This project addresses the problem of constructing statistical models of such data sets using examples from the data itself. The researchers will study the technical problems associated with constructing statistical modeling in high-dimensional spaces from mathematical and computational points of view. This research will focus on applications of these methods to problems in multidimensional image analysis, including denoising, segmentation, and image synthesis. This project will develop new algorithms for analyzing large sets of data. These algorithms make very weak assumptions about the statistical structure of data, and instead learn the statistics through large sets of examples, using raw measurements from very high dimensional spaces. The project combines a small team of researchers from probability theory, applied mathematics, and computer science to simultaneously address several important, fundamental questions pertaining to estimates of high-dimensional probability density functions, the computational challenges associated with these estimations, and the applications of these ideas to ongoing problems in science and medicine. The work in probability theory addresses basic questions about probability density functions in very high dimensional spaces. The applied mathematics work is developing methods for approximating these densities through lower-dimensional or sparse representations. The computer science research is examining implementation issues and the application of these methods to a wide range of ongoing problems that demand better algorithms for data analysis.