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Self-Similar Random Vector Fields and Their Wavelet Analysis

P.D. Tafti, M. Unser

Proceedings of the SPIE Optics and Photonics 2009 Conference on Mathematical Methods: Wavelet XIII, San Diego CA, USA, August 2-6, 2009, vol. 7446, pp. 74460Y-1/74460Y-8.



This paper is concerned with the mathematical characterization and wavelet analysis of self-similar random vector fields. The study consists of two main parts: the construction of random vector models on the basis of their invariance under coordinate transformations, and a study of the consequences of conducting a wavelet analysis of such random models. In the latter part, after briefly examining the effects of standard wavelets on the proposed random fields, we go on to introduce a new family of Laplacian-like vector wavelets that in a way duplicate the covariant-structure and whitening relations governing our random models.


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