Representations of two-dimensional acoustic velocity fields with Haar wavelets
Saulo Pomponet Oliveira, Emerson L. Gogola, Jorge V. R. Bonato, Wilson M. Figueiró · 2013
We present three algorithms for the representation of two-dimensional velocity fields with Haar wavelets and compare their efficiency in data compression. These approaches are: 1) to recast the 2D field as a 1D signal, compute its Haar expansion, and map the 1D expansion back to the 2D domain; 2) to perform the tensor product of 1D wavelet bases in the x- and z-directions and to compute the expansion of the 2D field with respect to this tensorial basis; and 3) to build a multi-resolution analysis from the two-dimensional Haar scaling function and to find the orthogonal complements between adjacent levels. We test these approaches on a synthetic acoustic velocity field.