PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes
This addresses the challenge of coupled restoration tasks in analytical chemistry, offering an incremental improvement over existing methods.
The paper tackles the joint problem of trend removal and blind deconvolution for sparse peak-like signals in analytical chemistry by proposing PENDANTSS, which combines sparse penalties and a source separation algorithm, resulting in a tool that outperforms comparable methods.
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.