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Two-dimensional quaternion wavelet transform. (English) Zbl 1232.65192
Summary: 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.

MSC:
65T50 Numerical methods for discrete and fast Fourier transforms
65T60 Numerical methods for wavelets
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