Two-dimensional quaternion wavelet transform

Publication year: 2011
Source: Applied Mathematics and Computation, In Press, Corrected Proof, Available online 14 June 2011

Mawardi, Bahri , Ryuichi, Ashino , Rémi, Vaillancourt

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets.