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Analyse comparative d'algorithmes de restauration en architecture dépliée pour des signaux chromatographiques parcimonieux

Mouna Gharbi, Silvia Villa, Emilie Chouzenoux, Jean-Christophe Pesquet, Laurent Duval

TL;DR

The paper tackles the reconstruction of sparse chromatographic signals from degraded observations by comparing three unfolded architectures derived from classical optimization methods. Using a parameterized, realistic data generator and HAL-inspired metrics for peak morphology, it shows that the U-HQ architecture outperforms U-PD and U-ISTA in MSE, SNR, TSNR, and peak-height/area/localization accuracy, while also offering faster computation. A parametric dataset toolbox enables systematic analysis of how sparsity, peak overlap, and noise affect performance, providing a practical resource for reproducibility. These findings support the adoption of unfolded semi-quadratic methods for efficient, interpretable chromatographic signal restoration in analytical chemistry.

Abstract

Data restoration from degraded observations, of sparsity hypotheses, is an active field of study. Traditional iterative optimization methods are now complemented by deep learning techniques. The development of unfolded methods benefits from both families. We carry out a comparative study of three architectures on parameterized chromatographic signal databases, highlighting the performance of these approaches, especially when employing metrics adapted to physico-chemical peak signal characterization.

Analyse comparative d'algorithmes de restauration en architecture dépliée pour des signaux chromatographiques parcimonieux

TL;DR

The paper tackles the reconstruction of sparse chromatographic signals from degraded observations by comparing three unfolded architectures derived from classical optimization methods. Using a parameterized, realistic data generator and HAL-inspired metrics for peak morphology, it shows that the U-HQ architecture outperforms U-PD and U-ISTA in MSE, SNR, TSNR, and peak-height/area/localization accuracy, while also offering faster computation. A parametric dataset toolbox enables systematic analysis of how sparsity, peak overlap, and noise affect performance, providing a practical resource for reproducibility. These findings support the adoption of unfolded semi-quadratic methods for efficient, interpretable chromatographic signal restoration in analytical chemistry.

Abstract

Data restoration from degraded observations, of sparsity hypotheses, is an active field of study. Traditional iterative optimization methods are now complemented by deep learning techniques. The development of unfolded methods benefits from both families. We carry out a comparative study of three architectures on parameterized chromatographic signal databases, highlighting the performance of these approaches, especially when employing metrics adapted to physico-chemical peak signal characterization.
Paper Structure (6 sections, 4 equations, 3 figures, 3 tables)

This paper contains 6 sections, 4 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Modèle de données et évaluation
  3. Travaux analogues
  4. Algorithmes
  5. Résultats
  6. Conclusions

Figures (3)

  • Figure 1: Observation bruitée ${\mathbf{z}}\xspace$ d'une somme de pics ${\mathbf{p}}\xspace$.
  • Figure 2: Caractérisation d'un pic : hauteur ($H$), aire ($A$), localisation ($L$). Support ($S$) et aire colorée (bleu) déterminés en fonction d'un seuil sur $H$ (ici $H/20$).
  • Figure 3: Diagrammes de dispersion $(\overline{{\mathbf{H}}\xspace},\hat{{\mathbf{H}}\xspace})$ des hauteurs des pics, parcimonie variable pour $D0$, $D1$ et $D2$ (1re, 2e et 3e lignes), pour U-HQ, U-ISTA et U-PD de gauche à droite.