@inproceedings {821,
	title = {Hierarchical posterior sampling for Gauss-Markov random fields},
	booktitle = {2003 International Conference on Image Processing},
	year = {2003},
	abstract = {<p>The estimation of images and random fields from sparse and/or noisy data is highly-developed, to the point where methods such as least-squares estimation, simulated annealing, and wavelet shrinkage are quite standardized. The key problem, however, is that the estimates are not a realistic version of the random field, and do not represent a typical or representative sample of the system being studied. Instead, what is often desired is that we find a random sample from the posterior distribution, a much more subtle and difficult problem than estimation. Typically this is solved using Markov-Chain Monte-Carlo / simulated annealing approaches, however these may be computationally challenging and slow to converge. In this paper we use hierarchical models to formulate a novel, fast posterior sampler.</p>
},
	keywords = {image estimation, image hierarchical posterior sampling, image sampling, least squares approximations, least-squares estimation, Markov processes, Markov-chain, Monte Carlo methods, Monte-Carlo method, noisy data, posterior distribution, random field, simulated annealing, wavelet shrinkage},
	doi = {http://dx.doi.org/10.1109/ICIP.2003.1247088},
	author = {P Fieguth}
}
@inproceedings {533,
	title = {Modeling the correlation structure of images in the wavelet domain},
	booktitle = {14th Canadian Conference on Electrical and Computer Engineering},
	year = {2001},
	address = {Toronto},
	abstract = {<p>In this paper we investigate the correlation structure of the wavelet coefficients corresponding to random fields. The context of this work is the study of Bayesian approaches to wavelet shrinkage for the purposes of image denoising. This paper concentrates on both within-scale and across-scale statistical dependencies for a variety of wavelets and random fields, with examples provided for both 1-D and 2-D signals. The results show the whitening effect of the wavelet transform to be quite clear-even for particular highly correlated spatial processes the within-scale correlation decays exponentially fast, however the correlation between scales is surprisingly substantial, even for separations several scales apart. Our goal, initiated in this paper, is the development of an efficient random field model, describing these statistical correlations, and the demonstration of its effectiveness in the context of Bayesian wavelet shrinkage for signal and image denoising</p>
},
	keywords = {1-D signals, 2-D signals, across-scale statistical dependencies, Bayes methods, Bayesian approaches, correlation structure, correlation theory, Image Denoising, image enhancement, random field model, random fields, wavelet coefficients, wavelet domain, wavelet shrinkage, wavelet transforms, white noise, whitening effect, within-scale statistical dependencies},
	doi = {http://dx.doi.org/10.1109/CCECE.2001.933599},
	author = {Z Azimifar and P Fieguth and E Jernigan}
}
