Related papers: Generalized Line Spectral Estimation via Convex Op…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks.…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…
We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
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…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimation problem is reduced to the problem of solving a stochastic monotone variational inequality (VI). The solution to the stochastic VI…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements. We propose to estimate the signals…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms…
In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral…