A note on the sampling of zero crossings of two-dimensional signals

Curtis et al. applied a theorem due to Bezout to show that almost all continuous, periodic, band-limited two-dimensional signals can be reconstructed from at most 4(N1+ N2)²zero-crossing samples where N1and N2is the number of Fourier coefficients in the signal. In this letter we prove a new version of Bezout´s theorem and apply it to the above problem to provide a more lenient sampling requirement of at most 8N1N2zero-crossing samples.