Many tasks in machine learning and signal processing can be solved by minimizing a
convex function of a measure. This includes sparse spikes deconvolution or training a …

This paper develops a mathematical theory of super‐resolution. Broadly speaking, super‐
resolution is the problem of recovering the fine details of an object—the high end of its …

This paper studies sparse spikes deconvolution over the space of measures. We focus on
the recovery properties of the support of the measure (ie, the location of the Dirac masses) …

This paper showcases the theoretical and numerical performance of the Sliding Frank–
Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super …

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical
problem arising, eg, in sparse spikes deconvolution or two-layer neural networks training …

This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from
noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a …

We consider the problem of recovering a signal consisting of a superposition of point
sources from low-resolution data with a cutoff frequency. If the distance between the sources …

The problem of direction of arrival (DOA) estimation has been studied for decades as an
essential technology in enabling radar, wireless communications, and array signal …

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) …

I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field
imaging of spatially incoherent optical sources. For any object too small to be resolved by …