Fast and L₂-optimal recovery for periodic nonuniformly sampled bandlimited signal

Uniformly-sampled sequence reconstruction from periodic nonuniform samples is addressed. In this problem setting, a bandlimited continuous-time signal is sampled with the same rate and different time offsets to obtain the periodic nonuniform samples, in which time offset information is unknown. We use a modified sequential forward selection algorithm to determine the sampling pattern corresponding to the time offset information, aiming to keep the condition number of the related matrix as small as possible. In our proposed algorithm, the reconstruction is formulated as a L₂-norm optimization problem. Besides, proper matrix partition is included to reduce the complexity of large matrix pseudo-inverse. Numerical examples are presented to demonstrate the effectiveness of the derived reconstruction algorithm and its stability problem, even in the presence of noise.