Sparse Approximations for Quaternionic Signals

作者：Barthelemy Quentin^*; Larue Anthony; Mars Jerome I

来源：Advances in Applied Clifford Algebras, 2014, 24(2): 383-402.

DOI：10.1007/s00006-013-0437-x

• Quaternionic signal processing
• sparse approximation
• orthogonal matching pursuit

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 quaternion noncommutativity, two quaternionic extensions are presented: the right-multiplication quaternionic OMP, which can be used to process right-multiplication linear combinations of quaternionic signals; and the left-multiplication quaternionic OMP, which can be used to process left-multiplication linear combinations. As validation, these quaternionic OMP algorithms are applied to simulated data. Denoising and deconvolution are carried out and presented here using a new spikegram that is designed for visualization of quaternionic coefficients. Finally these quaternionic OMPs are compared to multivariate OMP.

• 出版日期2014-6
• 单位中国地震局