One-dimensional MODE algorithm for two-dimensional frequency estimation

This paper describes how the computationally efficient one-dimensional MODE (1D-MODE) algorithm can be used to estimate the frequencies of two-dimensional complex sinusoids. We show that the 1D-MODE algorithm is computationally more efficient than the asymptotically statistically efficient 2D-MODE algorithm, especially when the numbers of spatial measurements are large. We find that the 1D-MODE algorithm is asymptotically statistically efficient for high signal-to-noise ratio. We also show that although the 1D-MODE is no longer statistically efficient when the number of temporal snapshots is large, the performance of the 1D-MODE can still be very close to that of the 2D-MODE under mild conditions. Numerical examples comparing the performance of the 1D-MODE and 2D-MODE algorithms are also presented.