Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d × d dilation matrix M , we demonstrate in a constructive way that we can construct compactly supported tight M -wavelet frames and orthonormal M -wavelet bases in L2(R) of exponential decay, which are derived from compactly supported M -refinable functions,...

An elementary proof of a basic uncertainty principle concerning pairs of representations of vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the impro...

This paper considers the design of wavelet tight frames based on iterated oversampled lter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grr obner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-tree DWT of Kingsbury, one goal is ...

We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.

This paper proposes an ortho-diffusion decomposition of graphs for estimating motion from image sequences. Orthonormal decompositions of the adjacency matrix representations of image data are alternated with diffusions and data subsampling in order to robustly represent image features using undirected graphs. Modified Gram-Schmidt with pivoting the columns algorithm is applied recursively for t...

The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for . We consider general (redundant) dictionaries for , and derive sufficient conditions for having uniquesparserepresentations of signals insuchdictionaries.Thespecial case where the dictionary is given by the union of ...

In a complex vector space of dimension N , by a full set of mutually unbiased bases (MUB’s) we mean a set of N+1 orthonormal bases such that the modulus square of the scalar product of any member of one basis with any member of any other basis is equal to 1/N . If we take e to denote the k vector in the α orthonormal basis, then having a full set of MUB’s amounts to having a collection e ; α = ...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...