Spectrum-blind minimum-rate sampling and reconstruction of 2-D multiband signals

We consider 2-D multiband signals, with a given bound on their spectral occupancy (the occupied fraction of the area of a bounding box of the spectral support). We propose a universal sampling pattern that guarantees well-conditioned reconstruction of all such signals. Such a universal sampling pattern can asymptotically achieve the Nyquist-Landau (1967) minimal sampling rate, determined by the spectral occupancy. Compared to 'Nyquist' patterns that avoid aliasing, for sparse spectral supports our design offers considerable reduction in sampling rate. Furthermore, we propose algorithms allowing reconstruction to be done blindly-without prior knowledge of the spectral support, other than its bounding box. The results apply to both continuous and discrete-time signals, and directly generalize to M-D. This work extends our analogous results for the 1D case.