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)
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
βpβ/βqβ 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.Comment: in French languag