TY - JOUR
T1 - Super-resolution on the sphere using convex optimization
AU - Bendory, Tamir
AU - Dekel, Shai
AU - Feuer, Arie
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - This paper considers the problem of recovering an ensemble of Diracs on a sphere from its low resolution measurements. The Diracs can be located at any location on the sphere, not necessarily on a grid. We show that under a separation condition, one can recover the ensemble with high precision by a three-stage algorithm, which consists of solving a semi-definite program, root finding and least-square fitting. The algorithm's computation time depends solely on the number of measurements, and not on the required solution accuracy. We also show that in the special case of non-negative ensembles, a sparsity condition is sufficient for recovery. Furthermore, in the discrete setting, we estimate the recovery error in the presence of noise as a function of the noise level and the super-resolution factor.
AB - This paper considers the problem of recovering an ensemble of Diracs on a sphere from its low resolution measurements. The Diracs can be located at any location on the sphere, not necessarily on a grid. We show that under a separation condition, one can recover the ensemble with high precision by a three-stage algorithm, which consists of solving a semi-definite program, root finding and least-square fitting. The algorithm's computation time depends solely on the number of measurements, and not on the required solution accuracy. We also show that in the special case of non-negative ensembles, a sparsity condition is sufficient for recovery. Furthermore, in the discrete setting, we estimate the recovery error in the presence of noise as a function of the noise level and the super-resolution factor.
KW - Harmonic analysis
KW - compressed sensing
KW - signal resolution
UR - http://www.scopus.com/inward/record.url?scp=84926435748&partnerID=8YFLogxK
U2 - 10.1109/TSP.2015.2399861
DO - 10.1109/TSP.2015.2399861
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AN - SCOPUS:84926435748
SN - 1053-587X
VL - 63
SP - 2253
EP - 2262
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 9
M1 - 7029667
ER -