Optimal choice of Hankel-block-Hankel matrix shape in 2-D parameter estimation: The rank-one case

In this paper we analyse the performance of 2-D ESPRIT method for estimating parameters of 2-D superimposed damped exponentials. 2-D ESPRIT algorithm is based on low-rank decomposition of a Hankel-block-Hankel matrix that is formed by the 2-D data. Through a first-order perturbation analysis, we derive closed-form expressions for the variances of the complex modes, frequencies and damping factors estimates in the 2-D single-tone case. This analysis allows to define the optimal parameters used in the construction of the Hankel-block-Hankel matrix. A fast algorithm for calculating the SVD of Hankel-block-Hankel matrices is also used to enhance the computational complexity of the 2-D ESPRIT algorithm.