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

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Publication

PENDANTSS Matlab code toolbox

Denoising, detrending and deconvolution with BEADS/SPOQ smooth/non-convex penalty with quasi-norm/norm ratios for peak-like signals
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 lp/lq 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.
Keywords Blind deconvolution, sparse signal, trend estimation, non-convex optimization, forward-backward splitting, alternating minimization, source separation

References