Event
Fundamental limits of compressed sensing under quantized measurements
Friday, March 10, 2017
3:00 p.m.
AVW 2168
Vinay Boda
2404856503
praneeth@umd.edu
Abstract: We study the limits of compression in terms of bits using a compressive sensing (CS) system. Namely, we consider the problem of recovering a sparse high-dimensional random vector from a quantized or lossy compressed version of its noisy random linear projections. The goal is to characterize the excess distortion incurred in encoding the source as a function of the number of measurements, sparsity, noise intensity, and the total number of bits in the compressed representation.
We first derive a single-letter expression describing the minimal mean square error (MSE) under optimal quantization in the large system limit. This characterization allows us to determine regimes where distortion is dominated by finite bit-precision rather than undersampling or noise. This optimal MSE, however, can only be achieved by first estimating the source before quantizing it. Arguably, in most cases, estimation before quantization is impossible due to computation constraints or unavailability of the random sampling matrix. As a result, one may attempt to describe the noisy observations rather than the original sparse source and later estimate the source from this description. By comparing the distortion in this scenario to the optimal MSE under quantization, we highlight regimes where estimation before quantization is highly beneficial and regimes where it is not.
Bio: Alon Kipnis is a Phd Candidate at Sanford University. Previously, he completed an M.Sc in mathematics, a B.Sc in electrical engineering and a B.Sc in Mathematics, all from Ben-Gurion University (BGU). His research interests include information theory, signal processing, wireless communication and statistical learning.
