D\'em\'elange, d\'econvolution et d\'ebruitage conjoints d'un mod\`ele convolutif parcimonieux avec d\'erive instrumentale, par p\'enalisation de rapports de normes ou quasi-normes liss\'ees (PENDANTSS)

TL;DR

PENDANTSS is a novel method that jointly performs trend removal and blind deconvolution of sparse signals, effectively separating noise and smooth trends using a combined sparse penalty and low-pass filtering.

Contribution

It introduces a new joint approach combining sparse penalties and low-pass filtering with a convergent optimization algorithm for signal restoration.

Findings

Outperforms existing methods on analytical chemistry signals

Efficient convergence with the Trust-Region block alternating approach

Reproducible code provided for implementation

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 pseudo-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: https://github.com/paulzhengfr/PENDANTSS.