MAP model order selection rule for 2-D sinusoids in white noise

We consider the problem of jointly estimating the number as well as the parameters of two-dimensional (2-D) sinusoidal signals, observed in the presence of an additive white Gaussian noise field. Existing solutions to this problem are based on model order selection rules and are derived for the parallel one-dimensional (1-D) problem. These criteria are then adapted to the 2-D problem using heuristic arguments. Employing asymptotic considerations, we derive a maximum a posteriori (MAP) model order selection criterion for jointly estimating the parameters of the 2-D sinusoids and their number. The proposed model order selection rule is strongly consistent. As an example, the model order selection criterion is applied as a component in an algorithm for parametric estimation and synthesis of textured images.

[1]  Petar M. Djuric,et al.  A model selection rule for sinusoids in white Gaussian noise , 1996, IEEE Trans. Signal Process..

[2]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  He Shuyuan.  Parameter estimation of hidden periodic model in random fields , 1999 .

[5]  Bin Zhou,et al.  Maximum likelihood estimation of 2-D superimposed exponential signals , 1994, IEEE Trans. Signal Process..

[6]  Debasis Kundu,et al.  Estimating the number of sinusoids in additive white noise , 1997, Signal Process..

[7]  G. M..  An Introduction to the Theory of Infinite Series , 1908, Nature.

[8]  T. A. Bromwich.  An Introduction To The Theory Of Infinite Series , 1908 .

[9]  Jorma Rissanen,et al.  Stochastic Complexity in Statistical Inquiry , 1989, World Scientific Series in Computer Science.

[10]  Torsten Söderström,et al.  Model-structure selection by cross-validation , 1986 .

[11]  J. M. Francos,et al.  A Wold-Like Decomposition of 2-D Discrete Homogeneous Random Fields , 1995 .

[12]  Josiane Zerubia,et al.  The two-dimensional Wold decomposition for segmentation and indexing in image libraries , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[13]  E. C. Titchmarsh,et al.  The Laplace Transform , 1991, Heat Transfer 1.

[14]  V. Umapathi Reddy,et al.  SVD-based information theoretic criteria for detection of the number of damped/undamped sinusoids and their performance analysis , 1993, IEEE Trans. Signal Process..

[15]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[16]  John W. Woods,et al.  Maximum likelihood parameter estimation of textures using a wold-decomposition based model , 1995, IEEE Transactions on Image Processing.

[17]  J. M. Francos,et al.  A Wold-Like Decomposition of Two-Dimensional Discrete Homogeneous Random Fields , 1995 .

[18]  George E. P. Box,et al.  Bayesian Inference in Statistical Analysis: Box/Bayesian , 1992 .

[19]  Joseph M. Francos,et al.  Strong consistency of a family of model order selection rules for estimating the parameters of 2D sinusoids in white noise , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[20]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[21]  Jian Li,et al.  Efficient mixed-spectrum estimation with applications to target feature extraction , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[22]  E. Hannan,et al.  DETERMINING THE NUMBER OF TERMS IN A TRIGONOMETRIC REGRESSION , 1994 .

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

[24]  B. G. Quinn,et al.  ESTIMATING THE NUMBER OF TERMS IN A SINUSOIDAL REGRESSION , 1989 .

[25]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .

[26]  E. J. Hannan,et al.  Estimating the dimension of a linear system , 1981 .

[27]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[28]  Z. Bai,et al.  On detection of the number of signals in presence of white noise , 1985 .