  Signal Reconstruction is one of the most important problem in signal
processing. This paper proposes a novel signal reconstruction method based on
the prolate spherical wave functions (PSWFs) and maximum correntropy criterion
(MCC). The PSWFs are a kind of special functions, which have been proved having
good performance in signal reconstruction. However, the existing PSWFs based
reconstruction methods only consider the mean square error (MSE) criterion as
the cost functions. The MSE criterion is sensitive to the non-Gaussian noise,
since it is builded up by the Gaussian assumption. Therefore, for the impulsive
noise or outliers, the MSE based reconstruction methods will lead to the large
reconstruction error. The proposed MCC and PSWFs based robust signal
reconstruction method can reduce the impact of large and non-Gaussian noise.
The experimental results on the synthetic signals show that the proposed method
can improve the MSE with notable gains in most cases.
