Abstract:

A method that attempts to recover signal using generalized
inverse theory is presented to obtain a good approximation
of the signal in reconstruction space from its generalized samples.
The proposed approaches differ with the assumptions on reconstruction
space. If the reconstruction space satisfies one-to-one
relationship between the samples and the reconstruction model,
then we propose a method, which achieves consistent signal reconstruction.
At the same time, when the number of samples is
more than the number of reconstruction functions, the minimalnorm
reconstruction signal can be obtained. Finally, it is demonstrated
that the minimal-norm reconstruction can outperform consistent
signal reconstruction in both theory and simulations for the
problem.

Key words: sampling, reconstruction, generalized inverse, shiftinvariant
space.