ISPSeminar

**Title:** "1930s Analysis for 2010s Signal Processing: Recent Progress on the Superresolution Question"

**Speaker:** Prof. Laurent Demanet, Imaging and Computing Group, MIT, USA (invited talk)

**Location:** "Shannon" Seminar Room, Place du Levant 3, Maxwell Building, 1st floor

**Date / Time (duration)**: Thursday 30/07/2015, 14h00 (~ 45')

**Abstract:** The ability to access signal features below the diffraction limit of an imaging system is a delicate nonlinear phenomenon called superresolution. The main theoretical question in this area is still mostly open: it concerns the precise balance of noise, bandwidth, and signal structure that enables super-resolved recovery. When structure is understood as sparsity on a grid, we show that there is a precise scaling law that extends Shannon-Nyquist theory, and which governs the asymptotic performance of a class of simple "subspace-based" algorithms. This law is universal in the minimax sense that no statistical estimator can outperform it significantly. By contrast, compressed sensing is in many cases suboptimal for the same task. Joint work with Nam Nguyen.

**Speaker's biography:** Laurent Demanet is Associate Professor of Applied Mathematics, Class of 1954 Career Development Chair, in the Department of Mathematics at MIT. He is also a member of MIT's Earth Resources Laboratory. Previously, he held a postdoctoral position called "Szego assistant professor" in the Department of Mathematics at Stanford. He obtained his Ph.D. in 2006 under Emmanuel Candes, in Applied and Computational Mathematics at Caltech. He completed his undergraduate studies in mathematical engineering and theoretical physics at Universite de Louvain, Belgium. He is the recipient of a Sloan research fellowship, a CAREER award from NSF, and a Young Investigator award from AFOSR. His research interests include applied analysis, scientific computing, inverse problems, and wave propagation.

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