We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is inappropriate. Thus the reasonable smoothing and regularized corrections are indispensable. In this paper, we propose several alternative methods for the signal reconstruction from the noisy multichannel samples under different smoothing and regularization principles. We compare these signal reconstruction methods theoretically and experimentally in the various situations. To demonstrate the effectiveness of the proposed methods, the probability interpretation and the error analysis for these methods are provided. Additionally, the numerical simulations as well as some guidelines to use the methods are also presented.

31 pages, 6 figures