Texture Boundary Detection Based on the Long Correlation Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling Textured Images Using Generalized Long Correlation Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Source separation in astrophysical maps using independent factor analysis
Neural Networks - 2003 Special issue: Neural network analysis of complex scientific data: Astronomy and geosciences
Digital Image Processing (3rd Edition)
Digital Image Processing (3rd Edition)
Toeplitz and circulant matrices: a review
Communications and Information Theory
Advanced Digital Signal Processing and Noise Reduction
Advanced Digital Signal Processing and Noise Reduction
Estimation and choice of neighbors in spatial-interaction models of images
IEEE Transactions on Information Theory
Noncausal Gauss Markov random fields: parameter structure and estimation
IEEE Transactions on Information Theory
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-similar texture modeling using FARIMA processes with applications to satellite images
IEEE Transactions on Image Processing
Long-correlation image models for textures with circular and elliptical correlation structures
IEEE Transactions on Image Processing
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In this paper, a parametric model for Gaussian random fields (GRFs) with long-correlation feature, namely the long correlation GRF (LC-GRF), is studied. Important properties of the model are derived and used for developing new parameter estimation algorithms and for constructing an optimum noise reduction filter. In particular, a novel iterative maximum likelihood estimation (MLE) algorithm is proposed for estimating the parameters of the model from a sample image, and the expectation-maximization (EM) algorithm is proposed for estimating the signal and noise variances given a noisy image. The optimal Wiener filter is derived making use of the parametric form of the model for the noise reduction under additive white Gaussian noise (WGN). Also the theoretic performance of the filter is obtained and its behavior is analyzed in terms of the long-correlation feature of the model. The effectiveness of the presented algorithms is demonstrated through experimental results on synthetic generated GRFs. An application to the restoration of cosmic microwave background (CMB) images in the presence of additive WGN is also presented.