相关论文: Peaks and jumps reconstruction with B-splines scal…

This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…

We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion…

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…

Inspired by shape constrained estimation under general nonnegative derivative constraints, this paper considers the B-spline approximation of constrained functions and studies the asymptotic performance of the constrained B-spline…

Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the…

Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…

We establish a theoretical connection between wavelet transforms and spiking neural networks through scale-space theory. We rely on the scale-covariant guarantees in the leaky integrate-and-fire neurons to implement discrete mother wavelets…

We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phase.…

A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines $\displaystyle{{\left({}^{\alpha}{\mathbf B}_{i}^{k} \right)}_{i=0}^{k}}$ which depends on an index $\alpha…

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ from its continuous short time Fourier transform…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…

This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions…

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…

This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…

This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a…

In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…

We present a new computationally efficient method for multi-beamforming in the broadband setting. Our "fast beamspace transformation" forms $B$ beams from $M$ sensor outputs using a number of operations per sample that scales linearly (to…

To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical…

The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…

We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…