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In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
Motivated by applications to multi-antenna wireless networks, we propose a distributed and asynchronous algorithm for stochastic semidefinite programming. This algorithm is a stochastic approximation of a continous- time matrix exponential…
Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We consider the problem of simultaneous reduction of acoustic echo, reverberation and noise. In real scenarios, these distortion sources may occur simultaneously and reducing them implies combining the corresponding distortion-specific…
A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a…
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest one and formally prove its convergence in…
Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest one and formally prove its convergence in…
This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the…
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…
In this note we work on the construction of positive preserving numerical schemes for systems of stochastic differential equations. We use the semi discrete idea that we have proposed before proposing now a numerical scheme that preserves…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new,…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…