Nonuniform decimation and reconstruction of generalized-bandlimited MD signals

It is well known that the data rate of bandlimited signals can be reduced without loss of information. One scheme which achieves this goal is the so-called nonuniform decimation. Recent results show that a bandlimited signal can be reconstructed from a nonuniformly decimated version. Theoretical results and efficient reconstruction methods have been addressed for one-dimensional signals. For the multidimensional case, some partial results are known. In this paper, we will discuss in detail the theory and implementation of the reconstruction of generalized-bandlimited multidimensional signals from their nonuniformly decimated versions.