000165374 001__ 165374
000165374 005__ 20190316235103.0
000165374 0247_ $$2doi$$a10.1109/TIP.2013.2249079
000165374 022__ $$a1057-7149
000165374 02470 $$2ISI$$a000318477500014
000165374 037__ $$aARTICLE
000165374 245__ $$aSparse image reconstruction on the sphere: implications of a new sampling theorem
000165374 269__ $$a2013
000165374 260__ $$bInstitute of Electrical and Electronics Engineers$$c2013$$aPiscataway
000165374 300__ $$a11
000165374 336__ $$aJournal Articles
000165374 520__ $$aA new sampling theorem on the sphere has been developed recently, reducing the number of samples required to represent a band-limited signal by a factor of two for equiangular sampling schemes. For signals sparse in a spatially localised measure, such as in a wavelet basis, overcomplete dictionary, or in the magnitude of their gradient, for example, a reduction in the number of samples required to represent a band-limited signal has important implications for sparse image reconstruction on the sphere. A more efficient sampling of the sphere improves the fidelity of sparse image reconstruction through both the dimensionality and spatial 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 (TV) inpainting, which relies on a sampling theorem to define a discrete TV norm on the sphere. Solving these problems is computationally challenging; hence we develop fast methods for this purpose. Numerical simulations are performed, verifying the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.
000165374 6531_ $$aLTS5
000165374 6531_ $$aCIBM-SP
000165374 6531_ $$aMIPLab
000165374 6531_ $$aLTS2
000165374 700__ $$0242931$$g201873$$aMcEwen, Jason
000165374 700__ $$0242927$$g179918$$aPuy, Gilles
000165374 700__ $$0240323$$g115534$$aThiran, Jean-Philippe
000165374 700__ $$0240428$$g120906$$aVandergheynst, Pierre
000165374 700__ $$0240173$$g152027$$aVan De Ville, Dimitri
000165374 700__ $$g163268$$aWiaux, Yves$$0240427
000165374 773__ $$j22$$tIEEE Transactions on Image Processing$$k6$$q2275-2285
000165374 8564_ $$uhttps://infoscience.epfl.ch/record/165374/files/css2_v4p1.pdf$$zn/a$$s613761$$yn/a
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000165374 937__ $$aEPFL-ARTICLE-165374
000165374 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000165374 980__ $$aARTICLE