Random Field Representation and Synthesis Using Wavelet Bases

Abstract

The paper addresses the representation and simulation of random fields using wavelet bases. The probabilistic description of the wavelet coefficients involved in the representation of the random field is discussed. It is shown that a broad class of random fields is amenable to a simplified representation. Further, it is shown that a judicious use of the local and multiscale structure of Daubechies wavelets leads to an efficient simulation algorithm. The synthesis of random field samples is based on a wavelet reconstruction algorithm which can be associated with a dynamic system in the scale domain. Implementation aspects are considered and simulation errors are estimated. Examples of simulating random fields encountered in engineering applications are discussed.