Sampling reconstruction of N-dimensional band-limited images after multilinear filtering

The generalized sampling expansion of A. Papoulis (1977) for a multichannel configuration is investigated for the case where the bandlimited input depends on N real-variables t₁ ,. . .,t_V and is used as a common input to a parallel bank of m independent N-dimensional linear shift-invariant filters. The input is assumed to have its N-dimensional Fourier transform bandlimited to the frequency range |ω_i|⩽σ_i: for i=1,2,. . .,N. If m, the number of channels, is written as a product of positive integers in the form m=m₁×m₂. . . m_N, then the bandlimited input can be completely reconstructed from samples taken at the filter outputs, each output being sampled at identical rates