TY - GEN
T1 - Sparse recovery of spherical harmonic expansions from uniform distribution on sphere
AU - Alem, Yibeltal F.
AU - Akramus Salehin, S. M.
AU - Chae, Daniel H.
AU - Kennedy, Rodney A.
PY - 2013
Y1 - 2013
N2 - We analyse the characteristics of spherical harmonics to derive a tighter bound on the minimum number of required measurements to accurately recover a sparse signal in spherical harmonic domain. We numerically show the coherence of spherical harmonic matrix can be reduced from a polynomial order of N 1/4 or N1/6 (both achieved by preconditioning) to a logarithmic order, i.e., log2(L) with respect to the degree of spherical harmonics L. Hence," one can, with high probability, recover s-sparse spherical harmonic expansions from M ≥ s log3 N measurements ra.ndomly sampled from the uniform sin θ dθ d φ measure on sphere.
AB - We analyse the characteristics of spherical harmonics to derive a tighter bound on the minimum number of required measurements to accurately recover a sparse signal in spherical harmonic domain. We numerically show the coherence of spherical harmonic matrix can be reduced from a polynomial order of N 1/4 or N1/6 (both achieved by preconditioning) to a logarithmic order, i.e., log2(L) with respect to the degree of spherical harmonics L. Hence," one can, with high probability, recover s-sparse spherical harmonic expansions from M ≥ s log3 N measurements ra.ndomly sampled from the uniform sin θ dθ d φ measure on sphere.
UR - http://www.scopus.com/inward/record.url?scp=84903849963&partnerID=8YFLogxK
U2 - 10.1109/ICSPCS.2013.6723949
DO - 10.1109/ICSPCS.2013.6723949
M3 - Conference contribution
SN - 9781479913190
T3 - 2013, 7th International Conference on Signal Processing and Communication Systems, ICSPCS 2013 - Proceedings
BT - 2013, 7th International Conference on Signal Processing and Communication Systems, ICSPCS 2013 - Proceedings
PB - IEEE Computer Society
T2 - 2013 7th International Conference on Signal Processing and Communication Systems, ICSPCS 2013
Y2 - 16 December 2013 through 18 December 2013
ER -