In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi{continuous wavelet transform of Mallat, steerable multiscale lters of Freeman and Adelson, and separable orthogonal and non{orthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the loc...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

A construction paradigm is proposed to refine a class of wavelet bases such that the filter characteristics are enhanced. In particular, it is shown that the entire Mth order B-wavelet family belong to this class. Exploiting some recent work, a fast integral wavelet transform is found for the refined B-wavelet family. Moreover, this refined basis can be placed into the setting of a multiresolut...

In this paper, we proposed a method for simultaneous noise suppression and decon-volution. The signal estimation and denoising problem was converted into a problem of model selection by using minimum description length(MDL) criterion to choose the best bases through a library of orthogonal bases. Deconvolution was then done in this best bases domain(actually the wavelet packet coeecients) to ac...

The fundamental ideas of wavelets are introduced within the context of mathematical physics. We present essential background notions of mathematical bases, and discuss Fourier, polynomial, and wavelets bases in this light. We construct several types of wavelets and wavelet-like bases and illustrate their use in algorithms for the solution of a variety of integral and di erential equations.

A novel method for learning optimal, orthonormal wavelet bases for representing 1and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities between these two concepts are reviewed and combined to a “wavenet”, allowing for the direct learning of optimal wavelet filter coefficient through stochastic gr...

The wavelet representation using orthonormal wavelet bases has received widespread attention. Recently M-band orthonormal wavelet bases have been constructed and compactly supported M-band wavelets have been parameterized 15, 12, 32, 17]. This paper gives the theory and algorithms for obtaining the optimal wavelet multiresolution analysis for the representation of a given signal at a predetermi...

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...