Self-similar random vector fields and their wavelet analysis
Pouya D. Tafti, Michael A. Unser · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
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.