• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Sparse Spikes Super-resolution on Thin Grids II: the Continuous Basis Pursuit

Duval, Vincent; Peyré, Gabriel (2017), Sparse Spikes Super-resolution on Thin Grids II: the Continuous Basis Pursuit. https://basepub.dauphine.fr/handle/123456789/17032

View/Open
Asymptotic-CBP.pdf (1.492Mb)
Type
Document de travail / Working paper
Date
2017
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
47
Metadata
Show full item record
Author(s)
Duval, Vincent cc
Peyré, Gabriel
Abstract (EN)
This article analyzes the performance of the Continuous Basis Pursuit (C-BP) method for sparse super-resolution. The C-BP has been recently proposed by Ekanadham, Tranchina and Simoncelli as a refined discretization scheme for the recovery of spikes in inverse problems regularization. One of the most well known discretization scheme, the Basis Pursuit (BP, also known as Lasso) makes use of a finite dimensional l1 norm on a grid. In contrast, the C-BP uses a linear interpolation of the spikes positions to enable the recovery of spikes between grid points. When the sought-after solution is constrained to be positive, a remarkable feature of this approach is that it retains the convexity of the initial l1 problem. The present paper shows how the C-BP is able to recover the spikes locations with sub-grid accuracy in the favorable case. We also prove that this regime generally breaks when the grid is too thin, and we describe precisely the artifacts that appear: each spike is approximated by a pair of Dirac masses. We show numerical illustrations of these phenomena, and evaluate numerically the validity of the technical assumptions of our analysis.
Subjects / Keywords
Continuous Basis Pursuit; asymptotic

Related items

Showing items related by title and author.

  • Thumbnail
    Sparse Spikes Deconvolution on Thin Grids 
    Duval, Vincent; Peyré, Gabriel (2015) Document de travail / Working paper
  • Thumbnail
    Support Recovery for Sparse Super-Resolution of Positive Measures 
    Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel (2016) Article accepté pour publication ou publié
  • Thumbnail
    The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy 
    Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel; Soubies, Emmanuel (2019) Article accepté pour publication ou publié
  • Thumbnail
    The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy 
    Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel; Soubies, Emmanuel (2018) Document de travail / Working paper
  • Thumbnail
    A Low-Rank Approach to Off-the-Grid Sparse Superresolution 
    Catala, Paul; Duval, Vincent; Peyré, Gabriel (2019) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo