Fast Implementation of Two-Dimensional APES and CAPON Spectral Estimators

The matched-filterbank spectral estimators APES and CAPON have recently received considerable attention in a number of applications. Unfortunately, their computational complexity tends to limit their usage in several cases – a problem that has previously been addressed by different authors. In this paper, we introduce a novel approach to the computation of the APES and CAPON spectra, which leads to a computational method that is considerably faster than all existing techniques. The new implementations of APES and CAPON are called fast APES and fast CAPON, respectively, and are developed for the two-dimensional case, with the one-dimensional case as a special case. Numerical examples are provided to demonstrate the application of APES to synthetic aperture radar (SAR) imaging, and to illustrate the reduction in computational complexity provided by our method.

[1]  Thomas G. Stockham,et al.  High-speed convolution and correlation , 1966, AFIPS '66 (Spring).

[2]  Petre Stoica,et al.  On Efficient Implementation of the Capon algorithm , 2000 .

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

[4]  Jian Li,et al.  Using APES for interferometric SAR imaging , 1998, IEEE Trans. Image Process..

[5]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

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

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

[8]  T. Moon,et al.  Mathematical Methods and Algorithms for Signal Processing , 1999 .

[9]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[10]  Jian Li,et al.  A new derivation of the APES filter , 1999, IEEE Signal Processing Letters.

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

[12]  Ali H. Sayed,et al.  Displacement Structure: Theory and Applications , 1995, SIAM Rev..

[13]  T. Kailath,et al.  Fast Parallel Algorithms for QR and Triangular Factorization , 1987 .

[14]  C. Rader.  An improved algorithm for high speed autocorrelation with applications to spectral estimation , 1970 .

[15]  Petre Stoica,et al.  Forward-only and forward-backward sample covariances - A comparative study , 1999, Signal Process..

[16]  J. Capon.  Maximum-likelihood spectral estimation , 1979 .

[17]  W. Rugh.  Linear System Theory , 1992 .

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

[19]  Thomas Kailath,et al.  Fast reliable algorithms for matrices with structure , 1999 .

[20]  Ali H. Sayed,et al.  Stabilizing the Generalized Schur Algorithm , 1996, SIAM J. Matrix Anal. Appl..

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

[22]  T. Kailath,et al.  A generalized Schur-type algorithm for the joint factorization of a structured matrix and its inverse , 1996 .

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

[24]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

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

[26]  Jian Li,et al.  An adaptive filtering approach to spectral estimation and SAR imaging , 1996, IEEE Trans. Signal Process..