BIVARIATE LOCAL TRIGONOMETRIC BASES ON TRIANGULARPARTITIONSKai

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...

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.

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...

Biorthogonal Local Trigonometric Bases

Algorithms for Trigonometric Curves (Simplification, Implicitization, Parameterization)

A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...