Multiband signal reconstruction from finite samples

The minimum mean-squared error (MMSE) estimator has been used to reconstruct a band-limited signal from its finite samples in a bounded interval and shown to have many nice properties. In this research, we consider a special class of band-limited 1-D and 2-D signals which have a multiband structure in the frequency domain, and propose a new reconstruction algorithm to exploit the multiband feature of the underlying signals. The concept of the critical value and region is introduced to measure the performance of a reconstruction algorithm. We show analytically that the new algorithm performs better than the MMSE estimator for band-limited/multiband signals in terms of the critical value and region measure. Finally, numerical examples of 1-D and 2-D signal reconstruction are given for performance comparison of various methods.