PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes

arXiv (Cornell University)

Abstract

Denoising, detrending, deconvolution: usual restoration tasks, traditionally decoupled. Coupled formulations entail complex ill-posed inverse problems. We propose PENDANTSS for joint trend removal and blind deconvolution of sparse peak-like signals. It blends a parsimonious prior with the hypothesis that smooth trend and noise can somewhat be separated by low-pass filtering. We combine the generalized quasi-norm ratio SOOT/SPOQ sparse penalties $\ell_p/\ell_q$ with the BEADS ternary assisted source separation algorithm. This results in a both convergent and efficient tool, with a novel Trust-Region block alternating variable metric forward-backward approach. It outperforms comparable methods, when applied to typically peaked analytical chemistry signals. Reproducible code is provided.

Authors 3

1. Paul Zheng Aachen

   RWTH Aachen University

   Affiliation as printed

   Rheinisch-Westfälische Technische Hochschule Aachen University

2. Émilie Chouzenoux

   Université Paris-Saclay · Institut national de recherche en sciences et technologies du numérique · CentraleSupélec

   Affiliation as printed

   Univ. Paris-Saclay , CentraleSupélec , CVN , Inria , Gif-sur-Yvette , France

3. Laurent C. Duval

   Université Paris-Saclay · Institut national de recherche en sciences et technologies du numérique · IFP Énergies nouvelles · CentraleSupélec

   Affiliation as printed

   Univ. Paris-Saclay , CentraleSupélec , CVN , Inria , Gif-sur-Yvette , France

   IFP Energies nouvelles