We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data co...

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and alwaysminimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately ...

We adress the problem of spherical deconvolution in a non parametric statistical framework, where both the signal and the operator kernel are subject to error measurements. After a preliminary treatment of the kernel, we apply a thresholding procedure to the signal in a second generation wavelet basis. Under standard assumptions on the kernel, we study the theoritical performance of the resulti...

Abstract— This paper introduces a new set of orthogonal moments function hypergeometric based on the discrete Legendre polynomials. The Legendre moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain o...

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ball...

in exploration seismology quality factor is widely used as a seismic attribute to identify anomalies related to attenuation, especially those caused by hydrocarbon. previous studies have indicated that seismic energy loss known as attenuation is greater for high frequency components of seismic data compared to the low frequency components. here the continuous wavelet transform is used to study ...

We have developed a tractometer: an online evaluation system for tractography processing pipelines. One can now evaluate the end effects on fiber tracts of different acquisition parameters (b-value, number of directions, denoising or not, averaging or not), different local estimation techniques (tensor, q-ball, spherical deconvolution, spherical wavelets) and to different tractography parameter...

Wavelets on the sphere are re-introduced and further developed independently of the original group theoretic formalism, in an alternative and completely equivalent approach, as inverse stereographic projection of wavelets on the plane. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB) anisotropies on the sky. In addition to off...

ABSTACT Experimental diiraction pole gure data are thought of as being discretely sampled from pole density functions P(h; r), i.e. even probability density functions deened on the cross-product S 2 S 2 of two unit spheres. Several useful representations of pole density functions exist which are usually related to speciic purposes: (i) series expansion into spherical harmonics, (ii) series expa...

Experimental diffraction pole figure data are thought of as being discretely sampled from pole density functions P(h, r), i.e. even probability density functions defined on the cross-product S2 x S2 of two unit spheres. Several useful representations of pole density functions exist which are usually related to specific purposes: (i) series expansion into spherical harmonics, (ii) series expansi...