Abstract
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.
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