Spike detection from inaccurate samplings

Abstract

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...) using an ${\ell }_1$-regularization procedure. In particular, we provide an explicit quantitative localization of the spikes.

Revised version, minor changes, 16pages

References in corpus (5)

• Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging
• Support detection in super-resolution
• Near Minimax Line Spectral Estimation
• Exact Support Recovery for Sparse Spikes Deconvolution
• Super-Resolution from Noisy Data

Cited by in corpus (4)

• Near Minimax Line Spectral Estimation
• Sparse Spikes Deconvolution on Thin Grids
• Super-resolution Line Spectrum Estimation with Block Priors
• Spectral Super-resolution With Prior Knowledge