@article {418, title = {Statistical processing of large image sequences}, journal = {IEEE Transactions on Image Processing}, volume = {14}, year = {2005}, pages = {80 - 93}, abstract = {

The dynamic estimation of large-scale stochastic image sequences, as frequently encountered in remote sensing, is important in a variety of scientific applications. However, the size of such images makes conventional dynamic estimation methods, for example, the Kalman and related filters, impractical. We present an approach that emulates the Kalman filter, but with considerably reduced computational and storage requirements. Our approach is illustrated in the context of a 512 times; 512 image sequence of ocean surface temperature. The static estimation step, the primary contribution here, uses a mixture of stationary models to accurately mimic the effect of a nonstationary prior, simplifying both computational complexity and modeling. Our approach provides an efficient, stable, positive-definite model which is consistent with the given correlation structure. Thus, the methods of this paper may find application in modeling and single-frame estimation.

}, keywords = {Algorithms, Artificial Intelligence, Automated, Biological, Cluster Analysis, computational complexity, Computer Graphics, Computer Simulation, Computer-Assisted, correlation methods, correlation structure, dynamic estimation method, image enhancement, image interpretation, image sequences, Imaging, Information Storage and Retrieval, Kalman filter, Kalman filters, large-scale stochastic image sequence estimation, Models, Movement, Numerical Analysis, ocean surface temperature, Pattern Recognition, Remote Sensing, Reproducibility of Results, Sensitivity and Specificity, Signal Processing, single-frame estimation, static estimation step, Statistical, statistical analysis, statistical image processing, stochastic processes, Subtraction Technique, Three-Dimensional, Video Recording}, issn = {1057-7149}, doi = {http://dx.doi.org/10.1109/TIP.2004.838703}, author = {F M. Khellah and P Fieguth and M J. Murray and M R. Allen} } @inproceedings {757, title = {Hierarchical Markov models for wavelet-domain statistics}, booktitle = {2003 IEEE Workshop on Statistical Signal Processing}, year = {2003}, abstract = {

There is a growing realization that modeling wavelet coefficients as statistically independent may be a poor assumption. Thus, this paper investigates two efficient models for wavelet coefficient coupling. Spatial statistics which are Markov (commonly used for textures and other random imagery) do not preserve their Markov properties in the wavelet domain; that is, the wavelet-domain covariance Pw does not have a sparse inverse. The main theme of this work is to investigate the approximation of Pw by hierarchical Markov and non-Markov models.

}, keywords = {correlation methods, hierarchical Markov models, image processing, Markov processes, spatial statistics, statistical analysis, wavelet coefficient coupling, wavelet transforms, wavelet-domain covariance, wavelet-domain statistics}, doi = {http://dx.doi.org/10.1109/SSP.2003.1289393}, author = {Z Azimifar and P Fieguth and E Jernigan} } @inproceedings {490, title = {A general multiresolution approach to the estimation of dense fields in remote sensing}, booktitle = {International Conference on Image Processing}, year = {1996}, address = {Lausanne, Switzerland}, abstract = {

A fast multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This multiscale algorithm produces solution and error estimates which are consistent with those obtained from exact least-squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least-squares, that is problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. Contrary to methods previously proposed for solving large least-squares problems, the multiscale approach provides error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations

}, keywords = {arbitrary measurement locations, computational cost, correlation methods, dense fields estimation, error estimates, error statistics, exact least-squares methods, fast multiscale optimal interpolation algorithm, general multiresolution approach, geophysical signal processing, hydrographic data mapping, hydrological techniques, image resolution, interpolation, least squares approximations, long-range correlations, measurements, multiscale algorithm, oceanographic data mapping, oceanographic techniques, Remote Sensing, workstation}, doi = {http://dx.doi.org/10.1109/ICIP.1996.560937}, author = {P Fieguth and A S. Willsky and D Menemenlis and C Wunsch} } @inproceedings {453, title = {Multiresolution model development for overlapping trees via canonical correlation analysis}, booktitle = {International Conference on Image Processing}, year = {1995}, abstract = {

A class of multiscale stochastic models has been introduced in which Gaussian random processes are described by scale-recursive dynamics that are indexed by the nodes of a tree. One of the primary reasons the framework is useful is that it leads to an extremely fast, statistically optimal algorithm for least-squares estimation in the context of 2-D images. We refine this approach to estimation by eliminating the visually distracting blockiness that has been observed in the previous work. We eliminate the blockiness by discarding the standard assumption that distinct nodes at a given level of our tree correspond to disjoint portions of the image domain; as a consequence of this simple idea, a given image pixel may now correspond to several tree nodes. We develop tools for systematically building overlapping-tree multiscale representations of prespecified statistics, and we develop a corresponding estimation algorithm for this processes. In this way, we achieve nearly optimal estimation results, we generate corresponding error covariance information, and we eliminate blockiness without sacrificing the resolution of fine-scale detail

}, keywords = {canonical correlation analysis, correlation methods, covariance analysis, error analysis, error covariance information, estimation algorithm, estimation theory, fast statistically optimal algorithm, Gaussian processes, Gaussian random processes, image domain, image pixel, image representation, image resolution, multiresolution model, multiscale representations, multiscale stochastic models, optimal estimation results, overlapping trees, random processes, scale recursive dynamics, statistics, tree nodes, trees (mathematics)}, doi = {http://dx.doi.org/10.1109/ICIP.1995.529035}, author = {P Fieguth and W W. Irving and A S. Willsky} }