Related papers: A note on spike localization for line spectrum est…

A fundamental small-noise sensitivity analysis of spike localization in the presence of adversarial perturbations and an arbitrary point spread function (PSF) is presented. The analysis leverages the local Lipschitz property of the inverse…

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This…

The power spectrum, as a statistic in Fourier space, is commonly numerically calculated using the fast Fourier transform method to efficiently reduce the computational costs. To alleviate the systematic bias known as aliasing due to the…

This article investigates the support detection problem using the LASSO estimator in the space of measures. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments...)…

We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…

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…

In many practical situations, the useful signal is contained in a low-dimensional subspace, drown in noise and interference. Many questions related to the estimation and detection of the useful signal arise. Because of their particular…

Theoretical results show that sparse off-the-grid spikes can be estimated from (possibly compressive) Fourier measurements under a minimum separation assumption. We propose a practical algorithm to minimize the corresponding non-convex…

In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…

This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…

We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…

The method of location and spectral estimation of weak signals on a noise background is being considered. The method is based on the optimized on order and noise dispersion autoregressive model of a sought signal. A new approach of model…

We consider the problem of detecting the presence of a signal in a rank-one spiked Wigner model. For general non-Gaussian noise, assuming that the signal is drawn from the Rademacher prior, we prove that the log likelihood ratio (LR) of the…

Spikes can be easily detected inmostintracellular recordings as sharp peaks. However, insome experimental preparations,because of unipolar morphology or other characteristicsof the recorded neurons, the sizes of the spikes recorded from the…

Determining the positions of neurons in an extracellular recording is useful for investigating functional properties of the underlying neural circuitry. In this work, we present a Bayesian modelling approach for localizing the source of…

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…

We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing…

We establish a theoretical connection between wavelet transforms and spiking neural networks through scale-space theory. We rely on the scale-covariant guarantees in the leaky integrate-and-fire neurons to implement discrete mother wavelets…

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…

Signals with single peak and symmetry property are very common in various fields, such as probability density function of normal distribution. Among the information contained in such signals, peak position is the most important, sometimes…