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In this paper, some algorithms for constructing tight wavelet frames on local fields using the unitary extension principles are suggested. We present a sufficient condition for finite number of functions to form a tight wavelet frame and establish general principles for constructing tight wavelet frames on local fields [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the continuous Bessel wavelet transformation and its inversion formula, and the Parseval relation using the theory of the Hankel convolution. A relation between the Bessel wavelet transformation and the Hankel–Hausdorff operator is established. [ABSTRACT FROM AUTHOR]

This paper deals with a construction of wavelet frame packets on the positive half-line ℝ+ using the splitting trick for frames. It is shown that, as long as finitely many splitting steps are applied, the resulting sequence of functions is a frame of L 2(ℝ+). If the matrix M(ξ) associated with the splitting is unitary, then the splitting can be applied infinitely many times to prove the existence of frame with the frame bounds as shown in Theorem 3.3. [ABSTRACT FROM AUTHOR]

This paper deals with a construction of dyadic wavelet frames on a positive half-line + using the Walsh-Fourier transform. We prove necessary and sufficient conditions for the system [image omitted] to be a wavelet frame in L2(+). These conditions are found to be better than those of Daubechies [Ten Lecture on Wavelets, NSF-CBMS Regional Conferences in Applied Mathematics, Vol. 61, SIAM, Philadelphia, PA, 1992], Chui and Shi [Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal. 24 (1993), pp. 263-277], Casazza and Christenson [Weyl-Heisenberg frames for subspaces of L2(), Proc. Amer. Math. Soc. 129 (2001), pp. 145-154] and Christenson [Frames, Riesz bases, and discrete Gabor/wavelet expansions, Bull. Amer. Math. Soc. 38 (2001), pp. 273-291; An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003]. [ABSTRACT FROM AUTHOR]

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for two popular models for the marginal posterior density. We also illustrate the superior performance of these models over the standard models for wavelet coefficients. [ABSTRACT FROM AUTHOR]

Presents a historical development of wavelet transforms, Gabor transforms and their myriad of mathematical, physical, medical, biological and engineering concepts, while discussing the existence of Fourier transforms and the Hilbert space formalism in wavelet transform analysis. Factors associated with the use of the Fourier transform of a signal; Details on Gabor transforms; Historical concept of wavelet transforms.

By the application of continuous wavelet transforms (or windowed Fourier transform) and employing Burzyk''s conjecture, the wavelet transform for integrable Boehmians is obtained. Inversion formula is also established. [Copyright &y& Elsevier]