Hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic textures

2012/10/06 by Abry, Patrice, Clausel, Marianne, Jaffard, Stéphane +2
#2010: 42C40 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1210.1944

Abstract

Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities constructed upon the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy. Its properties are studied in depth.

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