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