Optimized Local Trigonometric Bases

Biorthogonal Local Trigonometric Bases

Biorthogonal Smooth Local Trigonometric Bases

In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear components. We study and compare their approximation properties and applicability in data compression. This is illustrated with numerical examples.

BIVARIATE LOCAL TRIGONOMETRIC BASES ON TRIANGULARPARTITIONSKai

We construct bivariate local trigonometric bases on a \two-overlapping" triangular grid. A main result is the description of various trigonometric bases on triangles, satisfying parity conditions at the edges. Moreover, we introduce folding operators for the triangular grid. From these results we derive assertions on Riesz stability and the bi-orthogonal basis.

Fast Compression of Seismic Data with Local Trigonometric Bases

Our goal in this paper is to provide a fast numerical implementation of the local trigonometric bases algorithm1 in order to demonstrate that an advantage can be gained by constructing a biorthogonal basis adapted to a target image. Different choices for the bells are proposed, and an extensive evaluation of the algorithm was performed on synthetic and seismic data. Because of its ability to re...

Optimal Bell Functions for Biorthogonal Local Trigonometric Bases

A general approach for biorthogononal local trigonometric bases in the two-overlapping setting was given by Chui and Shi. In this paper, we give error estimates for the approximation with such basis functions. In particular, it is shown that for a partition of the real axis into small intervals one obtains better approximation order if polynomials are reproduced locally. Furthermore, smooth tri...