Quaternionic Sparse Approximation

Quentin Barthélemy (1, 2) , Anthony Larue (2) , Jerome I. Mars (1)

1 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
2 LOAD (CEA, LIST) - Laboratoire Outils d'Analyse des Données (CEA, LIST)

In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. We present a quaternionic extension, the quaternionic OMP, that can be used to process a right-multiplication linear combination of quaternionic signals. As validation, this quaternionic OMP is applied to simulated data. Deconvolution is carried out and presented here with a new spikegram that is designed for visualization of quaternionic coefficients, and finally this is compared to multivariate OMP.

Mots clés: sparse coding; statistical analysis; signal processing; quaternionic signal; quaternionic OMP; orthogonal matching pursuit (OMP); Spikegram; Deconvolution; multivariate OMP

Domaines: Traitement du signal et de l'image [eess.SP]

Quentin Barthélemy, Anthony Larue, Jerome I. Mars. Quaternionic Sparse Approximation. AGACSE 2012 - 5th conference on Applied Geometric Algebras in Computer Science and Engineering, Jul 2012, La Rochelle, France. Paper#4, p1-11. ⟨hal-00730188⟩