Sparse image reconstruction on the sphere: implications of a new sampling theorem

Jason D McEwen, Gilles Puy, Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Van De Ville, Yves Wiaux

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

Original languageEnglish
Article number6471228
Pages (from-to)2275-2285
Number of pages11
JournalIEEE Transactions on Image Processing
Volume22
Issue number6
DOIs
Publication statusPublished - Jun 2013

Keywords

  • Compressive sensing
  • harmonic analysis
  • sampling methods
  • spheres

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Medicine(all)

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