Metric Dependent Clifford Analysis with Applications to Wavelet Analysis
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In earlier research multi-dimensional wavelets have been constructed in the framework of Clifford analysis. Clifford analysis, centered around the notion of monogenic functions, may be regarded as a direct and elegant generalization to higher dimension of the theory of the holomorphic functions in the complex plane. This Clifford wavelet theory might be characterized as isotropic, since the metric in the underlying space is the standard Euclidean one.
In this paper we develop the idea of a metric dependent Clifford analysis leading to a so-called anisotropic Clifford wavelet theory featuring wavelet functions which are adaptable to preferential, not necessarily orthogonal, directions in the signals or textures to be analyzed.
KeywordsContinuous Wavelet Transform Clifford analysis Hermite polynomials
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