Two-dimensional nonparametric spectral analysis in the missing data case

We consider two-dimensional (2D) nonparametric complex spectral estimation (with its 1D counterpart as a special case) of data matrices with missing samples occurring in arbitrary patterns. Previously, the MAPES-EM algorithms were developed for the general 1D missing-data problem and shown to have excellent spectral estimation performance. In this paper, we present 2D extensions of MAPES-EM and develop another 2D MAPES algorithm, referred to as MAPES-CM, which solves a maximum likelihood problem iteratively via cyclic maximization (CM). Compared with MAPES-EM, MAPES-CM has similar spectral estimation performance but is computationally much more efficient.

[1]  Thomas L. Marzetta,et al.  Nonparametric spectral analysis with missing data via the EM algorithm , 2004 .

[2]  Benjamin Friedlander,et al.  ARMA spectral estimation of time series with missing observations , 1984, IEEE Trans. Inf. Theory.

[3]  Yonina Rosen,et al.  Optimal ARMA parameter estimation based on the sample covariances for data with missing observations , 1989, IEEE Trans. Inf. Theory.

[4]  Jian Li,et al.  Nonparametric spectral analysis with missing data via the EM algorithm , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[5]  Andreas Jakobsson,et al.  Cisoid parameter estimation in the colored noise case: asymptotic Cramer-Rao bound, maximum likelihood, and nonlinear least-squares , 1997, IEEE Trans. Signal Process..

[6]  R. Bos,et al.  Estimation of autoregressive spectra with randomly missing data , 2003, Proceedings of the 20th IEEE Instrumentation Technology Conference (Cat. No.03CH37412).

[7]  Petre Stoica,et al.  Statistical analysis of two nonlinear least-squares estimators of sine-wave parameters in the colored-noise case , 1989 .

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

[9]  Erik G. Larsson,et al.  Amplitude spectrum estimation for two-dimensional gapped data , 2002, IEEE Trans. Signal Process..

[10]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[11]  Erik G. Larsson,et al.  Fast Implementation of Two-Dimensional APES and CAPON Spectral Estimators , 2002, Multidimens. Syst. Signal Process..

[12]  P. Stoica,et al.  Cyclic minimizers, majorization techniques, and the expectation-maximization algorithm: a refresher , 2004, IEEE Signal Process. Mag..

[13]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

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

[15]  Erik G. Larsson,et al.  Adaptive Filter-bank Approach to Restoration and Spectral Analysis of Gapped Data* , 2000 .

[16]  Jian Li,et al.  Spectral analysis of periodically gapped data , 2003 .

[17]  J. Högbom,et al.  APERTURE SYNTHESIS WITH A NON-REGULAR DISTRIBUTION OF INTERFEROMETER BASELINES. Commentary , 1974 .

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