title: Sparse image reconstruction on the sphere: implications of a new sampling theorem.
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.
authors.affiliation: Department of Physics and Astronomy, University College London, London WC1E 6BT, UK. jason.mcewen@ucl.ac.uk
authors.forename: Jason D
authors.initials: JD
authors.lastname: McEwen
authors.forename: Gilles
authors.initials: G
authors.lastname: Puy
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Thiran
authors.forename: Pierre
authors.initials: P
authors.lastname: Vandergheynst
authors.forename: Dimitri
authors.initials: D
authors.lastname: Van De Ville
authors.forename: Yves
authors.initials: Y
authors.lastname: Wiaux
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003952:Diagnostic Imaging; D005843:Geography; D007091:Image Processing, Computer-Assisted / Q000379:methods*