Summer 2019

Wed, July 31st 2019, 2:00PM, Venue: Hamerschlag D210
Maxime Ferreira Da Costa, CMU

Title: The resolution limits of spike deconvolution using total variation

Abstract:Inferring the fine scale properties of a signal from its coarse measurements is a common signal processing task that finds a myriad of applications in various areas of experimental sciences. Super-resolution is probably one of the most iconic problem in this category, and aims to recovering the locations of highly localized temporal patterns, or spikes, from Fourier domain measurements. This problem has been empirically known for years to become ill-posed when the distance between the spikes to reconstruct crosses the Rayleigh resolution limit. Recent advances have shown that convex programming could be used to robustly estimate the spikes by minimizing the total variation over the set of measures. We give a review of this estimation framework, and discuss the resolution limits of the total variation estimator. In particular, we show the existence of phase transitions on its consistency and on its stability, based on the minimal separation between the spikes. We further extend the total variation method to tackle the blind deconvolution problem, and highlight similar phase transition phenomena.

Bio: Maxime Ferreira Da Costa received the Ph.D. degree in Electrical and Electronic Engineering from Imperial College London, UK, in 2018. He was awarded the M.Sc in Signal Processing from Imperial College London in 2012, and the Diplôme d'Ingénieur from CentraleSupélec, France, the same year. Since Fall 2018, he is a Research Associate with the department of Electrical and Computer Engineering at Carnegie Mellon University. His research focuses on signal processing, harmonic analysis, and optimization with application to sensing systems and data science.