@article {524,
	title = {Multiply-rooted multiscale models for large-scale estimation},
	journal = {IEEE Transactions on Image Processing},
	volume = {10},
	year = {2001},
	pages = {1676 - 1686},
	abstract = {<p>Divide-and-conquer or multiscale techniques have become popular for solving large statistical estimation problems. The methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems, each more straightforward than the original. However this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound, leading to problems of computational complexity and numerical stability. In this paper, we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided, and the problem is instead addressed piece-by-piece. The approach possesses promising attributes: it is not a local method-the estimate at every point is based on all measurements; it is numerically stable for problems of arbitrary size; and the approach retains the benefits of the multiscale framework on which it is based: a broad class of statistical models, a stochastic realization theory, an algorithm to calculate statistical likelihoods, and the ability to fuse local and nonlocal measurements</p>
},
	keywords = {asymptotically large problems, computational complexity, conditional decorrelation, estimation theory, geophysical signal processing, hierarchical estimation, image processing, large statistical estimation problems, large-scale estimation, local measurements fusion, multiply-rooted multiscale models, multiscale framework, nonlocal measurements fusion, numerical stability, oceanographic techniques, Remote Sensing, statistical analysis, statistical likelihoods, statistical models, stochastic realization theory},
	issn = {1057-7149},
	doi = {http://dx.doi.org/10.1109/83.967396},
	author = {P Fieguth}
}
@inproceedings {511,
	title = {Foveated multiscale models for large-scale estimation},
	booktitle = {International Conference on Image Processing},
	year = {1999},
	abstract = {<p>Efficient, large-scale estimation methods such as nested dissection or multiscale estimation rely on a divide-and-conquer strategy, in which a statistical problem is conditionally broken into smaller pieces. This conditional decorrelation is not possible for arbitrarily large problems due to issues of computational complexity and numerical stability. Given the growing interest in global-scale-remote sensing problems (or even three-dimensional problems), in this summary we develop a class of estimators with more promising asymptotic computational properties</p>
},
	keywords = {asymptotic computational properties, computational complexity, conditional decorrelation, decorrelation, divide and conquer methods, divide-and-conquer strategy, foveated multiscale models, global-scale-remote sensing problems, image processing, large-scale estimation methods, multiscale estimation, nested dissection, numerical stability, statistical problem, three-dimensional problems},
	doi = {http://dx.doi.org/10.1109/ICIP.1999.823022},
	author = {P Fieguth}
}
