EE Seminar: Compressed sensing under optimal quantization
(The talk will be given in English)
Speaker: Dr. Alon Kipnis
Department of Statistics, Stanford University
Sunday, March 25th, 2018
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
Compressed sensing under optimal quantization
Abstract
A number of theoretical and experimental results have shown that generally speaking, compressed sensing with quantization can perform well if the signal is very sparse, the noise is very low, and the bit-rate is sufficiently large. However, a precise characterization of the fundamental tradeoffs between these quantities has remained elusive.
Building upon ideas from statistical physics and random matrix theory, we provide single-letter formulas for the reconstruction error associated with optimal decoding under three specific quantization schemes: (1) estimate-and-compress source coding strategy where the signal is first estimated and then compressed with respect to the asymptotic distribution of finite subsets given the measurements. (2) compress-and-estimate where the measurements are quantized with respect to a Gaussian codebook and the sparse signal is estimated at the decoder, and (3) power-aware compress-and-estimate, where a Gaussian codebook is used in a rotated coordinate system.
These quantization schemes are shown to be optimal in some problem regimes, and hence the aforementioned single-letter expressions provide explicit characterizations of the minimal mean-squared error as a function of the average quantization bit-rate, the spectral distribution of the sensing matrix, and the prior distribution of the signal.
Short bio
Alon Kipnis received the B.Sc. degree in mathematics, the B.Sc. degree in electrical engineering and the M.Sc in mathematics, all from Ben-Gurion University of the Negev. He recently received the Ph.D degree in electrical engineering from Stanford University, and he is currently a postdoctoral scholar at the Department of Statistics there. His research focuses on the intersection of data compression, signal processing and machine learning.
