On the global convergence of gradient descent for over-parameterized models using optimal transport
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 …
convex function of a measure. This includes sparse spikes deconvolution or training a …
Towards a mathematical theory of super‐resolution
EJ Candès… - Communications on pure …, 2014 - Wiley Online Library
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 …
resolution is the problem of recovering the fine details of an object—the high end of its …
Exact support recovery for sparse spikes deconvolution
V Duval, G Peyré - Foundations of Computational Mathematics, 2015 - Springer
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) …
the recovery properties of the support of the measure (ie, the location of the Dirac masses) …
The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy
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 …
Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super …
Sparse optimization on measures with over-parameterized gradient descent
L Chizat - Mathematical Programming, 2022 - Springer
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 …
problem arising, eg, in sparse spikes deconvolution or two-layer neural networks training …
Near minimax line spectral estimation
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 …
noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a …
Super-resolution of point sources via convex programming
C Fernandez-Granda - Information and Inference: A Journal of …, 2016 - academic.oup.com
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 …
sources from low-resolution data with a cutoff frequency. If the distance between the sources …
A new atomic norm for DOA estimation with gain-phase errors
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 …
essential technology in enabling radar, wireless communications, and array signal …
[HTML][HTML] Spike detection from inaccurate samplings
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) …
space of measures. More precisely, we study the recovery of a discrete measure (spike train) …
Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
M Tsang - New Journal of Physics, 2017 - iopscience.iop.org
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 …
imaging of spatially incoherent optical sources. For any object too small to be resolved by …