Multichannel Sampling of Multidimensional Parametric Signals

The contribution of this paper is two-fold; first, we present a novel approach for sampling and reconstructing two dimensional signals with parametric structure or namely signals with Finite Rate of Innovation (FRI). The considered signals are bi-level polygons and set of 2-D Diracs and it will be shown that with the use of ACMP method, projection-slice theorem, Radon projections and exponential splines as sampling kernels, such signals can be perfectly reconstructed. Then, we present a possible extension of the theory of sampling multidimensional FRI signals, discussed above, to the case of multichannel acquisition systems. The essential issue of our considered multichannel system is that each channel receives the input signal with an unknown geometric transformation which needs to be estimated. We pose both the synchronization stage and the signal reconstruction stage as a parametric estimation problem and demonstrate that a simultaneous exact synchronization of the channels and reconstruction of the FRI signal is possible.