Random wavelet transformation and its properties
Tomasz R. Bielecki, Jie Chen, Stephen S.‐T. Yau · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
A discrete random wavelet transformation is defined as a random field of stochastic integrals of translates and dilates of a compactly supported wavelet function with respect to a fractional Brownian motion. It is shown that the transformation exhibits several properties analogous to the ones demonstrated previously for the `classical' wavelet transformation of a fractional Brownian motion. Moreover, some important advantages of the transformation defined here, over its `classical' counterpart, are demonstrated.