Related papers: Well-Posedness of Sparse Frequency Estimation
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…
In the theory of compressed sensing (CS), the sparsity ||x||_0 of the unknown signal x\in\R^p is commonly assumed to be a known parameter. However, it is typically unknown in practice. Due to the fact that many aspects of CS depend on…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to…
Accurate acoustic simulations of enclosed spaces require precise boundary conditions, typically expressed through surface impedances for wave-based methods. Conventional measurement techniques often rely on simplifying assumptions about the…
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…
In this work we explore the possibility of using sparse statistical modeling in condensed matter physics. The procedure is employed to two well known problems: elemental superconductors and heavy fermions, and was shown that in most cases…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…