Multiplicative and additive perturbation effects on the recovery of sparse signals on the sphere using compressed sensing

In this paper, we show how perturbation can affect the reconstruction of sparse spherical harmonic (SH) signals, whose domain is the sphere, with compressed sensing (CS) techniques. Our results show that the multiplicative perturbation, which can be generated by the jitter of the sampling locations (co-latitude and longitude) of the signal, can cause significant error in the SH-signal recovery with compressed sensing. To apply compressed sensing practically to the reconstruction of SH-signal, the method of calibration to minimize the multiplicative perturbation is suggested. Furthermore, we showed that the possibility of noise reduction in SH-signal reconstruction with a diversity technique which combines multiple sparse recoveries.