Testing Gaussian Process with Applications to Super-Resolution - Archive ouverte HAL Access content directly
Journal Articles Applied and Computational Harmonic Analysis Year : 2018

Testing Gaussian Process with Applications to Super-Resolution

(1) , (2, 3) , (4)
1
2
3
4

Abstract

This article introduces exact testing procedures on the mean of a Gaussian process $X$ derived from the outcomes of $\ell_1$-minimization over the space of complex valued measures. The process $X$ can thought as the sum of two terms: first, the convolution between some kernel and a target atomic measure (mean of the process); second, a random perturbation by an additive (centered) Gaussian process. The first testing procedure considered is based on a dense sequence of grids on the index set of $X$ and we establish that it converges (as the grid step tends to zero) to a randomized testing procedure: the decision of the test depends on the observation $X$ and also on an independent random variable. The second testing procedure is based on the maxima and the Hessian of $X$ in a grid-less manner. We show that both testing procedures can be performed when the variance is unknown (and the correlation function of $X$ is known). These testing procedures can be used for the problem of deconvolution over the space of complex valued measures, and applications in frame of the Super-Resolution theory are presented. As a byproduct, numerical investigations may demonstrate that our grid-less method is more powerful (it detects sparse alternatives) than tests based on very thin grids.
Fichier principal
Vignette du fichier
Azais18_Testing_Gaussian_Process.pdf (5.59 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01686434 , version 1 (02-07-2018)

Identifiers

Cite

Jean-Marc Azaïs, Yohann de Castro, Stéphane Mourareau. Testing Gaussian Process with Applications to Super-Resolution. Applied and Computational Harmonic Analysis, 2018. ⟨hal-01686434⟩
453 View
202 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More