Related papers: Multivariate Exponential Analysis from the Minimal…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
Prony's method, in its various concrete algorithmic realizations, is concerned with the reconstruction of a sparse exponential sum from integer samples. In several variables, the reconstruction is based on finding the variety for a zero…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…
The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of…
Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this…
Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior…
The matrix pencil method is an eigenvalue based approach for the parameter identification of sparse exponential sums. We derive a reconstruction algorithm for multivariate exponential sums that is based on simultaneous diagonalization.…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational structure of their Fourier coefficients and reconstructing…
Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…