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arXiv · 2307.01761

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)

Paul Zheng·Emilie Chouzenoux·Laurent Duval
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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.

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Paul Zheng, Emilie Chouzenoux, Laurent Duval. 2023-07-04. 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). https://arxiv.org/abs/2307.01761

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