We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames. ∗This work was supported by ...

Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The results of the compression change as per the basis and tap of the wavelet used. This paper compares compression performance of Daubechies, Biorthogonal, Coiflets and other wavelets along with res...

there are a variety of electrocardiogram (ecg) based methods to detect myocardial infarction (mi) patients. this study used the signal averaged electrocardiogram (saecg) and its wavelet coefficient as an index to detect mi. orthogonal leads signals from 50 acute myocardial infarction (ami) and 50 healthy subjects were selected from the national metrology institute of germany (ptb diagnostic dat...

In this paper, we investigate the use of compactly supported divergencefree wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in detail the bases and corresponding fast algorithms for 2D and 3D incompressible flows. In order to compute the nonlinear term, we propose a new method which provid...

For a nonlinear functional f , and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f(u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree structure. Applications are found in the field of (adaptive) tensor product solution methods for semilinear op...

The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of ...

We construct orthonormal wavelet bases of L2(IR) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H2 of all two-dimensional (2D) scaling coefficients satisfying the orthogonality condition as an implicit function. This set includes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H2 at HN , the scaling coefficients...

Following the approach of Chui and Quak, we investigate semi-orthogonal spline wavelets on the unit interval [0, 1]. We give a slightly different construction of boundary wavelets. As a result, we are able to prove that the inner wavelets and the newly constructed boundary wavelets together constitute a Riesz basis for the wavelet space at each level with the Riesz bounds being level-independen...

We construct orthonormal wavelet bases of L 2 (IR 2) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H 2 of all 2d scaling coeecients satisfying the orthogonality condition as an implicit function. This set includes the scaling coeecients for the induced 1d wavelets. We compute the tangent space of H 2 at H N , the scaling coeecients for the indu...

The rise of frame theory in appled mathematics is due to the flexibility and redundancy of frames. Structured frames are much easier to construct than Structured orthonormal bases. In this work, the notion of the ternary generalized multiresolution structure (TGMS) of subspace 2 3 ( ) L R is proposed, which is the generalization of the ternary frame multiresolution analysis. The biorthogonality...