Robust Deconvolution with Parseval Filterbanks

Rossen Nenov, Vincent Lostanlen, Peter Balazs

Session: General

Keywords: Deconvolution, digital signal processing, gradient methods, signal reconstruction, sparse approximation

TL;DR: The paper introduces Multi-RDCP, a regularization method promoting subband sparsity, and SNAKE, an algorithm for faster deconvolution in noisy signals. SNAKE achieves fast convergence rates, supported by theoretical proofs and numerical experiments.

Abstract: This article introduces two contributions: Multiband Robust Deconvolution (Multi-RDCP), a regularization approach for deconvolution in the presence of noise; and Subband-Normalized Adaptive Kernel Evaluation (SNAKE), a first-order iterative algorithm designed to efficiently solve the resulting optimization problem. Multi-RDCP resembles Group LASSO in that it promotes sparsity across the subband spectrum of the solution. We prove that SNAKE enjoys fast convergence rates and numerical simulations illustrate the efficiency of SNAKE for deconvolving noisy oscillatory signals.

Submission Number: 94