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18 February 2025
 
  » arxiv » 2301.01514

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PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes
Paul Zheng ; Emilie Chouzenoux ; Laurent Duval ;
Date 4 Jan 2023
AbstractDenoising, 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.
Source arXiv, 2301.01514
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