Efficient implementation of the 2-D Capon spectral estimator

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. 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. (see IEEE Trans. Aerosp. Electron. Syst., vol.34, no.4, p.1314-19, October 1998).

[1]  Charles W. Therrien,et al.  A direct algorithm for computing 2-D AR power spectrum estimates , 1989, IEEE Trans. Acoust. Speech Signal Process..

[2]  Stuart R. DeGraaf,et al.  SAR imaging via modern 2-D spectral estimation methods , 1998, IEEE Trans. Image Process..

[3]  Bede Liu,et al.  An efficient algorithm for two-dimensional autoregressive spectrum estimation , 1989, IEEE Trans. Acoust. Speech Signal Process..

[4]  J. P. Burg,et al.  Maximum entropy spectral analysis. , 1967 .

[5]  T. Kailath,et al.  Efficient inversion of Toeplitz-block Toeplitz matrix , 1983 .

[6]  Bruce R. Musicus.  Fast MLM power spectrum estimation from uniformly spaced correlations , 1985, IEEE Trans. Acoust. Speech Signal Process..

[7]  Jian Li,et al.  Performance analysis of forward-backward matched-filterbank spectral estimators , 1998, IEEE Trans. Signal Process..

[8]  E. Robinson,et al.  Recursive solution to the multichannel filtering problem , 1965 .

[9]  Andreas Jakobsson,et al.  Computationally efficient two-dimensional Capon spectrum analysis , 2000, IEEE Trans. Signal Process..

[10]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[11]  J. Capon.  High-resolution frequency-wavenumber spectrum analysis , 1969 .

[12]  O. Strand.  Multichannel complex maximum entropy (autoregressive) spectral analysis , 1977 .

[13]  Petre Stoica,et al.  Two-Dimensional Capon Spectrum Analysis , 1999 .

[14]  L. Ljung,et al.  New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices , 1979 .

[15]  J.H. McClellan,et al.  Multidimensional spectral estimation , 1982, Proceedings of the IEEE.

[16]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[17]  D. Manolakis,et al.  Fast algorithms for block toeplitz matrices with toeplitz entries , 1984 .

[18]  P. Whittle.  On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix , 1963 .

[19]  Jian Li,et al.  Efficient implementation of Capon and APES for spectral estimation , 1998 .

[20]  Andreas Jakobsson.  Model-Based and Matched-Filterbank Signal Analysis , 1999 .

[21]  Dan E. Dudgeon,et al.  Multidimensional Digital Signal Processing , 1983 .

[22]  Philip N. Borer,et al.  Application of the maximum likelihood method to a large 2D NMR spectrum using a parallel computer , 1989 .

[23]  Rangaraj M. Rangayyan,et al.  An algorithm for direct computation of 2-D linear prediction coefficients , 1993, IEEE Trans. Signal Process..

[24]  Andreas Jakobsson,et al.  Matched-filter bank interpretation of some spectral estimators , 1998, Signal Process..

[25]  S. D. Stearns,et al.  Digital Signal Analysis , 1976, IEEE Transactions on Systems, Man, and Cybernetics.