Construction of Biorthogonal Wavelet Packets on Local Fields of Positive Characteristic

TL;DR

This paper constructs biorthogonal wavelet packets on local fields of positive characteristic, addressing symmetry issues in wavelet analysis for signal processing applications.

Contribution

It introduces a new method for constructing biorthogonal wavelet packets on local fields of positive characteristic and explores their properties via Fourier transforms.

Findings

New Riesz bases of L2(K) constructed

Algorithms for decomposition and reconstruction provided

Enhanced symmetry properties in wavelet packets achieved

Abstract

Orthogonal wavelet packets lack symmetry which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by the biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of the Fourier transforms. We also show how to obtain several new Riesz bases of the space L2(K) by constructing a series of subspaces of these wavelet packets. Finally, we provide the algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.