Related papers: Partial parameterization of orthogonal wavelet mat…
As a generalization of orthonormal wavelets in $L_2(R)$, tight framelets (also called tight wavelet frames) are of importance in wavelet analysis and applied sciences due to their many desirable properties in applications such as image…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
Orthogonal wavelets, or wavelet frames, for L^2(R) are associated with quadrature mirror filters (QMF). The latter constitute a set of complex numbers which relate the dyadic scaling of functions on R to the Z-translates, and which satisfy…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
It is given an efficient complete parametrization of wavelet matrices of rank $m$, genus $g+1$, and degree $g$, which are naturally identified with corresponding polynomial paraunitary matrix-functions. The parametrization depends on…
We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
For a natural number d and a d-dimensional real vector r let Tau(r) denote the (d-dimensional) shift radix system associated with r. Tau(r) is said to have the finiteness property iff all orbits of Tau(r) end up in the zero vector; the set…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…
When Fourier series are used for applications in physics, involving partial differential equations, sometimes the process of resolution results in divergent series for some quantities. In this paper we argue that the use of linear low-pass…
Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the…
The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N>=4 admits an affine orbit. This settles a recent open problem…
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and…
This paper proposes a equivariant filtering (EqF) framework for the inertial-integrated state estimation problem. As the kinematic system of the inertial-integrated navigation can be naturally modeling on the matrix Lie group $SE_2(3)$, the…
This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
Many navigation problems can be formulated as observer design on linear observed systems with a two-frame group structure, on which an invariant filter can be implemented with guaranteed consistency and stability. It's still unclear how…