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

DOI:
10.60864/d51t-xc92
Citation Author(s):
Paul Zheng; Emilie Chouzenoux; Laurent Duval
Submitted by:
LAURENT DUVAL
Last updated:
6 June 2024 - 10:27am
Document Type:
Poster
Document Year:
2024
Event:
Presenters:
ZHENG, Paul
Paper Code:
SPTM-P10.10
 

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 Smoothed One-Over-Two/Smoothed p-Over- q (SOOT/SPOQ) sparse penalties $l_p/l_q$ with the Baseline Estimation And Denoising with Sparsity (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.

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