Balanced approximation of stochastic systems
SIAM Journal on Matrix Analysis and Applications
Neural networks for signal processing
Neural networks for signal processing
SIAM Journal on Scientific Computing
Adaptation of spectral trajectory models for large vocabulary continuous speech recognition
Adaptation of spectral trajectory models for large vocabulary continuous speech recognition
Efficient multiresolution counterparts to variational methods for surface reconstruction
Computer Vision and Image Understanding
A tutorial on learning with Bayesian networks
Learning in graphical models
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Internal multiscale autoregressive processes, stochastic realization, and covariance extension
Internal multiscale autoregressive processes, stochastic realization, and covariance extension
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 06
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 02
Fractal estimation using models on multiscale trees
IEEE Transactions on Signal Processing
Hierarchical stochastic modeling of SAR imagery forsegmentation/compression
IEEE Transactions on Signal Processing
Multiscale autoregressive models and wavelets
IEEE Transactions on Information Theory
The modeling and estimation of statistically self-similar processes in a multiresolution framework
IEEE Transactions on Information Theory
Multiscale segmentation and anomaly enhancement of SAR imagery
IEEE Transactions on Image Processing
An overlapping tree approach to multiscale stochastic modeling and estimation
IEEE Transactions on Image Processing
Multiscale methods for the segmentation and reconstruction of signals and images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally efficient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. Our realization theory and algorithms addresses these issues by focusing on the estimation-theoretic concept of predictive efficiency and by exploiting the scale-recursive structure of so-called internal MAR processes. Our realization algorithm has complexity quadratic in problem size and with an approximation we also obtain an algorithm that has complexity linear in problem size.