Structured signal recovery without the shackles of convexity

When
Start: 09/21/2016 - 4:15pm
End  : 09/21/2016 - 5:15pm

Category
Colloquium

Speaker
Mahdi Soltanolkotabi (USC)

Abstract

Many problems in science and engineering ask for solutions to underdetermined systems of linear equations. The last decade has witnessed a flurry of activity in understanding when and how it is possible to solve such problems using convex/greedy schemes. Structured signal recovery via convex methods has arguably revolutionized signal acquisition, enabling signals to be measured with remarkable fidelity using a small number of measurements. Despite many success stories, in this talk I will argue that over insistence on convex methods has stymied progress in some application domains. I will discuss my ongoing research efforts to “unshackle” structured signal recovery from the confines of convexity opening the door for new applications. In particular, I will present a unified theoretical framework for sharply characterizing the convergence rates of various (non-)convex iterative schemes for solving such problems. Time permitting, I will also discuss problem domains where carefully designed non-convex techniques are effective but convex counterparts are known to fail or yield suboptimal results. This is based on joint work with collaborators who shall be properly introduced during the talk.

Where
Kravis Center Lower Court 62, Claremont McKenna College