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

TL;DR

PENDANTSS is a novel method that jointly removes trends and deconvolves sparse signals by combining sparse penalties with low-pass filtering, outperforming existing methods in analytical chemistry signal processing.

Contribution

It introduces a convergent, efficient joint trend removal and blind deconvolution method using a new optimization approach and sparse penalties, with demonstrated superior performance.

Findings

Outperforms comparable methods on analytical chemistry signals

Provides a convergent and efficient optimization algorithm

Reproducible code is available for implementation

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 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.