Construction of Quaternion-Valued Wavelets

Abstract

In this paper, we introduce quaternion-valued wavelets in the context of the duplex matrix-valued function. We then formulate quaternion scaling and wavelet functions using quaternion multiresolution analysis (QMRA).With these formulations, we obtain coefficients of highpass and lowpass filters of QMRA. Keywords: Quaternion-valued wavelets; quaternion multiresolution analysis; highpass and lowpass filters.