we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provi...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provided.

Given a dilation matrix A : Z d → Z d , and G a complete set of coset representatives of 2π(A −− Z d /Z d), we consider polynomial solutions M to the equation g∈G M (ξ + g) = 1 with the constraints that M ≥ 0 and M (0) = 1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbol...

critical pulmonary valve stenosis (cpvs) and atrial septal defect (asd) is an uncommon form of congenital heart disease. concurrent transcatheter pulmonary valvuplasty and closure of secundum atrial septal defect appears to be an interesting alternative to surgical correction. we present the simultaneous balloon valvuloplasty of critical pulmonary stenosis (ps) with supra systemic right ventric...

For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all–important, since it governs the downsampling and upsampling steps, determines the cosets that give the positions of the filters, and defines the elementary set that gives a tesselation of the plane. We introduce nonseparable bidimensional wavelets, and give formulae for the analysis and synthesis of imag...

To construct a very smooth nonseparable multiscaling function, we impose polynomial approximation order 2 and add new conditions on the polyphase highpass filters. We work with a dilation matrix generating quincunx lattices, and fix the index set. Other imposed conditions are orthogonal filter bank and balancing. We construct a smooth, compactly supported multiscaling function and multiwavelet,...

Given a function ψ in L2(Rd), the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions {| det a|j/2ψ(ajx−γ) : j ∈ Z, γ ∈ Γ}. In this article we prove that the set of functions generating affine systems that are a Riesz basis of L2(Rd) is dense in L2(Rd). We also prove that a stronger result is true for affine systems that a...

This paper gives a practical method of extending an n× r matrix P (z), r ≤ n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z ∈ T, it can be extended to a matrix with nonvanishing dete...

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...