Related papers: A multivariate generalization of Prony's method
This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of…
This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…
The radii polynomial approach is an a posteriori validation method based on the contraction of a quasi-Newton operator. We apply this strategy to give a computer-assisted proof of a transverse heteroclinic orbit in the Shimizu--Morioka…
We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…
A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of…
For an arbitrary given span of high-dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampling set that allows for the unique reconstruction of each…
Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…