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One-Dimensional MODE Algorithm for Two-Dimensional Frequency Estimation

In this paper, we describe how the computationally efficientone-dimensional MODE (1D-MODE) algorithm can be used to estimatethe frequencies of two-dimensional complex sinusoids. We showthat the 1D-MODE algorithm is computationally more efficientthan the asymptotically statistically efficient 2D-MODE algorithm,especially when the numbers of spatial measurements are large.Interestingly enough, we prove that the 1D-MODE algorithm isasymptotically statistically efficient for high signal-to-noiseratio. We also show that although 1D-MODE is no longer statisticallyefficient when the number of temporal snapshots is large, theperformance of 1D-MODE can still be very close to that of the2D-MODE under mild conditions. Numerical examples comparing theperformances of the 1D-MODE and 2D-MODE algorithms are alsopresented.