Corpus ID: 7691378

Implications for compressed sensing of a new sampling theorem on the sphere

  title={Implications for compressed sensing of a new sampling theorem on the sphere},
  author={Jason D. McEwen and Gilles Puy and Jean-Philippe Thiran and Pierre Vandergheynst and Dimitri Van De Ville and Yves Wiaux},
A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a band-limited signal on the sphere exactly has important implications for compressed sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show the superior… Expand


A Novel Sampling Theorem on the Sphere
  • J. McEwen, Y. Wiaux
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 2011
This work develops a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension and highlights the advantages of the sampling theorem in the context of potential applications, notably in the field of compressive sampling. Expand
Computing Fourier Transforms and Convolutions on the 2-Sphere
This paper considers the problem of efficient computation of the spherical harmonic expansion, or Fourier transform, of functions defined on the two dimensional sphere, S^2. The resulting algorithmsExpand
Sparse recovery for spherical harmonic expansions
We show that sparse spherical harmonic expansions can be efficiently recovered from a small number of randomly chosen samples on the sphere. To establish the main result, we verify the restrictedExpand
Computing Fourier tran sforms and convolutions on the sphere
  • Advances in Applied Mathematics, vol. 15, pp. 202–250, 1994.
  • 1994