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

arXiv: https://arxiv.org/abs/2301.01514 · HTML: https://mlsanity.com/paper/2301.01514/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 30 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 2 of 2)

- [Convex Sparse Blind Deconvolution](https://mlsanity.com/paper/2106.07053/) (2021)
- [Sparse Signal Reconstruction for Nonlinear Models via Piecewise Rational Optimization](https://mlsanity.com/paper/2010.15427/) (2020)

## Abstract (arXiv)

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 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.