We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decomposition and reconstruction are considered as well as some stability-related questions. In addition, we briefly review the bivariate case for tensor produc...

This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of...

A brief survey of a paper by Peter Steffen, et al. Introduction G.K. Chesterton, an English author and journalist from the turn of the century, once stated he desired to write a story about a man setting sail from England in search of a new and foreign land. Eventually, when the man reached the island of his destination, he found it to be the most extraordinary and fascinating place. Unbeknowns...

In this paper a method is presented that parameterizes orthogonal wavelet transforms with respect to their properties (i.e. compact support, vanishing moments, regularity , symmetry) and also takes into considerations a simple implementation of the transform. The parameter space is given by the rotation angles of the orthogonal 2 2 rotations used in the lattice lters that realize the diierent s...

Search algorithms for finding signal decompositions called near-best bases using decision criteria called non-additive information costs have recently been proposed by Taswell [12] for selecting bases in wavelet packet transforms represented as binary trees. These methods are extended here to distinguish between top-down and bottom-up tree searches. Other new non-additive information cost funct...

We derive a learning algorithm for inferring an overcomplete basis by viewing it as probabilistic model of the observed data. Over-complete bases allow for better approximation of the underlying statistical density. Using a Laplacian prior on the basis coeecients removes redundancy and leads to representations that are sparse and are a nonlinear function of the data. This can be viewed as a gen...

In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...

In this paper we investigate compactly supported wavelet bases for Sobolev spaces. Starting with a pair of compactly supported refinable functions φ and φ̃ in L2(R) satisfying a very mild condition, we provide a general principle for constructing a wavelet ψ such that the wavelets ψjk := 2j/2ψ(2j · − k) (j, k ∈ Z) form a Riesz basis for L2(R). If, in addition, φ lies in the Sobolev space H(R), t...

There has been an important emergence of applications in which data arrives in an online time-varying fashion (e.g. computer network traffic, sensor data, web searches, ATM transactions) and it is not feasible to exchange or to store all the arriving data in traditional database systems to operate on it. For this kind of applications, as it is for traditional static database schemes, density es...