Back to Departmental Colloquium: Spring 2016
Departmental Colloquium
Date: Tuesday, Feb 23, 2016
Time: 4:00PM
Location: LCB 219
Veniamin Morgenshtern
Stanford University
Title |
Solving Underdetermined Linear Systems with Highly Correlated Columns |
Abstract |
This talk will consist of two parts. In the first part, I will review the simplest classical result on sparse signal recovery from incomplete data (compressed sensing). Underlying this result is the basic assumption that the columns of the measurment (design) matrix are only weakly correlated. This assumption is violated in many important applications. For example, in genetic data analysis, in super-resolution microscopy, and in radar imaging. In the second part of the talk, I will focus on super-resolution microscopy and on radar imaging and explain the conditions under which convex optimisation can solve the inverse problem in these cases. The analysis relies on novel constructions in Fourier analysis and on concentration inequalities for random matrices with specific structure. I will conclude with a brief discussion of a related open problem that is currently of great interest to me. |
Mathematical Biology
Computational Mathematics
Applied Mathematics