We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classification purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.

The rst part of this work describes the full set of Daubechies Wavelets with a particular emphasis on symmetric (and complex) orthonormal bases. Some properties of the associated complex scaling functions are presented in a second part. The third and last part describes a multiscale image enhancement algorithm using the phase of the complex multiresolution representation of the 2 dimension sign...

K.-H. Grr ochenig and A. Haas asked whether for every expanding integer matrix A 2 M n (Z) there is a Haar-type orthonormal wavelet basis having dilation factor A and translation lattice Z n. They proved that this is the case when the dimension n = 1. This paper shows that this is also the case when the dimension n = 2.

In this paper, a non iterative algorithm for the simultaneous identiication of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under weak assumptions on the persistency of excitation of the inputs, the algorithm provides consistent ...

The Ridgelet Packets library provides a large family of orthonormal bases for functions f(x, y) in L(dxdy) which includes orthonormal ridgelets as well as bases deriving from tilings reminiscent from the theory of wavelets and the study of oscillatory Fourier integrals. An intuitively appealing feature: many of these bases have elements whose envelope is strongly aligned along specified ‘ridges...

Calculations based on high-resolution quantizations prove that the distortion rate D( R) of an image transform coding is proportional to 2 2 R when R is large enough. In wavelet and block cosine bases, we show that if R < 1 bit/pixel, then D( R) varies like R1 2 , where remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. ...

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many ...

We consider ultrametric space with a measure, such that the measure of any ball is positive. A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable functions is introduced. Pseudodifferential operators (PDO) in the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and compute the...

A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to arbitrary measure functions on general (up to some topological restrictions) ultrametric space is introduced. Pseudodifferential operators (PDO) on the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and com...