New variational computational methods for modeling dual spaces of distributions, decomposition of functions, oscillations, and inverse problems in image analysis

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

The investigators will study new computational techniques with applications to inverse problems and image analysis. They will seek new methods that combine variational arguments with ideas from computational harmonic analysis and partial differential equations in order to overcome limitations of existing methods. The research will have three objectives: propose new models for cartoon and texture separation in images by working with spaces of distributions; propose completely new techniques for multiscale hierarchical decomposition of images; propose efficient algorithms for solving inverse problems. From the proposed research and educational program, computational mathematics, image processing, as well as more general areas of science and engineering will benefit. Applications include image analysis, medical imaging, satellite imaging, material science, and terrain data analysis, surveillance and inverse problems.