Construction of biorthogonal wavelet packets on local fields of positive characteristic

Authors: FIRDOUS AHMAD SHAH, MOHAMMAD YOUNUS BHAT

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 biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space $L^2(K)$ by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.

Keywords: Wavelet, multiresolution analysis, scaling function, wavelet packet, Riesz basis, local field, Fourier transform

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