Quaternionic analytic signal using atomic functions

Abstract

Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. In 1D signals, is usual to compute the phase and the magnitude of a signal using the analytic signal (the signal and its Hilbert transform using complex numbers). However, for high dimensional signals the monogenic signal (the signal and its Riesz transform) has been used to obtain the local phase and orientation with good results. The main aim of this work is to present a new way to make the computation of the Hilbert transform using the atomic function. The computation of the Hilbert transform take relevance when the phase computation is required. © 2012 Springer-Verlag.