Computationally efficient two-dimensional Capon spectrum analysis

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 with the one obtained by using the prediction matrix polynomials given by the Whittle–Wiggins–Robinson algorithm. Numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well-known classical implementation and the method recently published by Liu et al..