Multi-channel sampling and reconstruction of bandlimited two-dimensional signals

A deterministic two-dimensional bandlimited signal x(t₁, t₂) is used as a common input to m linear shift-invariant 2-D filters (channels). For m=m₁·m₂, the m channel outputs are `downsampled´ at rates in t<sub>1</sub> and t<sub>2</sub> that are reduced by factors of m<sub>1</sub> and m<sub>2</sub> respectively from the usual Nyquist rates required for input sample reconstruction. It is shown that if the transfer functions of the m-channels are `independent´, then the input x(t) is uniquely recoverable from the channel output samples taken at the indicated rates. Moreover, the recovery can be effected by the use of m linear shift-invariant post-filters