We present a computationally efficient algorithm for computing the 2-D Capon spectral estimator. The implementation is based on the fact that the 2-D data covariance matrix will have a Toeplitz-Block-Toeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg-Heinig formula that is a function of strictly the forward 2-D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the difference in the so-obtained 2-D spectral estimate as compared to the one obtained by using the prediction matrix polynomials given by the Whittle-Wiggins-Robinson algorithm. Numerical simulations illustrate the clear computational gain in comparison to both the well-known classical implementation and the method recently published by Liu et al.
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