Easy Path Wavelet Transform on Triangulations of the Sphere

The computation of sparse representations of data on the sphere (e.g. topographical data) is a crucial step for further processing such as multiple separation, migration, imaging and sparsity promoting data-recovery. The Easy Path Wavelet Transform (EPWT) is a new tool for sparse data representation that has recently been introduced for image compression. In this paper we consider the EPWT on spherical triangulations. It is a locally adaptive transform that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. In our approach the usual discrete one-dimensional orthogonal or biorthogonal wavelet transform can be applied. The EPWT can be used for defining a multiresolution analysis on the sphere in which the scaling spaces and the wavelet spaces depend adaptively on the data. Issues of implementation of the EPWT are also considered.