Analysis and synthesis methods in compressive signal processing

Applied and Computational Mathematics Seminar
Monday, April 28, 2014 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Deanna Needell – Claremont McKenna College –
Martin Short
In this talk we will discuss results for robust signal reconstruction from random observations via synthesis and analysis methods in compressive signal processing (CSP). CSP is a new and exciting field which arose as an efficient alternative to traditional signal acquisition techniques. Using a (usually random) projection, signals are measured directly in compressed form, and methods are then needed to recover the signal from those measurements. Synthesis methods attempt to identify the low-dimensional representation of the signal directly, whereas analysis type methods reconstruct in signal space. We also discuss special cases including provable near-optimal reconstruction guarantees for total-variation minimization and new techniques in super-resolution.