Performance Analysis of Discrete-valued Vector Reconstruction Based on Box-constrained Sum of L1 Regularizers
Ryo Hayakawa, Kazunori Hayashi
Abstract
In this paper, we analyze the asymptotic performance of a convex optimization-based discrete-valued vector reconstruction from linear measurements. We firstly propose a box-constrained version of the conventional sum of absolute values (SOAV) optimization, which uses a weighted sum of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularizers as a regularizer for the discrete-valued vector. We then derive the asymptotic symbol error rate (SER) performance of the box-constrained SOAV (Box-SOAV) optimization theoretically by using convex Gaussian min-max theorem. Simulation results show that the empirical SER performances of Box-SOAV and the conventional SOAV are very close to the theoretical result for Box-SOAV when the problem size is sufficiently large.
BibTeX
@inproceedings{icassp2019_performanceanaly,
title = {Performance Analysis of Discrete-valued Vector Reconstruction Based on Box-constrained Sum of L1 Regularizers},
author = {Ryo Hayakawa and Kazunori Hayashi},
booktitle = {ICASSP 2019},
year = {2019}
}