Near Maximal 2-D Sinusoid Identification From Limited Data

We describe a novel method to identify a large number of two-dimensional (2-D) sinusoids from very limited data. Starting with the noiseless exponential superposition model, we derive the 2-D linear prediction equations for the data, and present a general 2-D exponential identification algorithm based on one-dimensional (1-D) rooting techniques. Then we enhance this general algorithm for the special case of 2-D sinusoid identification by using conjugate-reverse data to increase the number of identifiable sinusoids and by using FFT to avoid polynomial rooting. Noise is handled by least-squares solutions of the linear prediction equations and the polynomial equations. Numerical simulations demonstrate that our algorithm provides a competitive alternative to existing algorithms