A Novel Smoothed Norm Ratio for Sparse Signal Restoration Application to Mass Spectrometry.

Afef Cherni (1) , Emilie Chouzenoux (2) , Laurent Duval (3) , Jean-Christophe Pesquet (4, 2)

1 I2M - Institut de Mathématiques de Marseille
2 OPIS - OPtimisation Imagerie et Santé
3 IFPEN - IFP Energies nouvelles
4 CVN - Centre de vision numérique

We propose a new smoothed p-Over-q norm ratio for sparse signal reconstruction. A trust-region Variable Metric Forward-Backward is proposed to solve efficiently the resulting non-convex minimization problem. Numerical experiments in the context of mass spectrometry (MS) illustrate the benefits of the novel penalty.

Mots clés: Sparsity; Non-convex optimization; SPOQ.; Ill-posed problem

Domaines: Sciences de l'ingénieur [physics]; Traitement du signal et de l'image [eess.SP]

Afef Cherni, Emilie Chouzenoux, Laurent Duval, Jean-Christophe Pesquet. A Novel Smoothed Norm Ratio for Sparse Signal Restoration Application to Mass Spectrometry.. SPARS 2019 - Signal Processing with Adaptive Sparse Structured Representations, Jul 2019, Toulouse, France. ⟨hal-02179379⟩