In [1], Beylkin et al. introduced a wavelet-based algorithm that approximates integral or matrix operators of a certain type by highly sparse matrices, as the basis for efficient approximate calculations. The wavelets best suited for achieving the highest possible compression with this algorithm are Daubechies wavelets, while Coiflets lead to a faster decomposition algorithm at slightly lesser ...

The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary circuits, further cementing the relation established in Refs. 1 and 2 between classical and quantum multi-scale methods. An algorithm for constructing the ci...

This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and their spectra are introduced here. The frequency detection properties of daublets are investigated through scalograms derived from these new analytical expres...

Explicit algorithms are presented for the generation of Daubechies compact orthogonal least asymmetric wavelet filter coefficients and the computation of their Holder regularity. The algorithms yield results for any number N of vanishing moments for the wavelets. These results extend beyond order N = 10 those produced by Daubechies for the values of the filter coefficients and those produced by...

Wave Cluster is a grid based clustering approach. Many researchers have applied wave cluster technique for segmenting images. Wave cluster uses wave transformation for clustering the data item. Normally it uses Haar, Daubechies and Cohen Daubechies Feauveau or Reverse Bi-orthogonal wavelets. Symlet, Biorthogonal and Meyer wavelet families have been used in this paper to compare its clustering c...

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l (1) regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the tempo...

Construction of higher multiplicity wavelets adapted to a particular task is discussed. The proposed method uses parameterization of wavelet matrices. Large classes of wavelet matrices are searched to minimize a given cost function on training data. The method is applied to a problem of detecting and possibly removing a disturbance of a certain kind from a signal. The importance of choosing the...

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...

w)I2 + [G(w + :)I' = 1. Its periodic extension then satisfies +*(w) 2 1 and hence a sampling function with q w) = +(w)/G*(w) belongs to L2(Z2). 5) Daubechies Wavelets: The scaling function for the simplest class of Daubechies wavelets, those with support on [0, 31, are defined by the dilation equations REFERENCES [ 11 I. Daubechies, " Orthonormal bases of compactly supported wavelets, " Comm. c...