Sparse Approximations for Quaternionic Signals

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 study, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions non-commutativity, two quaternionic extensions are presented: the right-multiplication quaternionic OMP, that can be used to process right-multiplication linear combinations of quaternionic signals, and the left-multiplication quaternionic OMP, that can be used to process left-multiplication linear combinations. As validation, these quaternionic OMP are 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 these are compared to multivariate OMP.

Mots clés: orthogonal matching pursuit.; sparse coding; spectrum analysis; signal deconvolution; sparse approximation; orthogonal matching pursuit; Quaternionic signal processing; signal processing

Domaines: Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]

Quentin Barthélemy, Anthony Larue, Jerome I. Mars. Sparse Approximations for Quaternionic Signals. Advances in Applied Clifford Algebras, 2014, 24 (2), pp.383-402. ⟨10.1007/s00006-013-0437-x⟩. ⟨hal-00874959⟩