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We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
The co-sparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary \Omega, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis…
This article analyzes the recovery performance of two popular finite dimensional approximations of the sparse spikes deconvolution problem over Radon measures. We examine in a unified framework both the L1 regularization (often referred to…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
This paper demonstrates that if the restricted isometry constant $\delta_{K+1}$ of the measurement matrix $A$ satisfies $$ \delta_{K+1} < \frac{1}{\sqrt{K}+1}, $$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover…
We consider the problem of recovering equations of motion from multivariate time series of oscillators interacting on sparse networks. We reconstruct the network from an initial guess which can include expert knowledge about the system such…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
In this note, we investigate the theoretical properties of Orthogonal Matching Pursuit (OMP), a class of decoder to recover sparse signal in compressed sensing. In particular, we show that the OMP decoder can give $(p,q)$ instance…
Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…
Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…
Greedy algorithms for feature selection are widely used for recovering sparse high-dimensional vectors in linear models. In classical procedures, the main emphasis was put on the sample complexity, with little or no consideration of the…
Direction of Arrival (DOA) estimation of mixed uncorrelated and coherent sources is a long existing challenge in array signal processing. Application of compressive sensing to array signal processing has opened up an exciting class of…
In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…