Abstract

A new approach to high-order-conditional probability density estimation is developed, based on a partitioning of conditioning space via decision trees. The technique is applied to image compression, image restoration, and texture synthesis, and the results compared with those obtained by standard mixture density and linear regression models. By applying the technique to subband-domain processing, some evidence is provided to support the following statement: the appropriate tradeoff between spatial and spectral localization in linear preprocessing shifts towards greater spatial localization when subbands are processed in a way that exploits interdependence.

Citations

6514	Elements of Information Theory - Cover, Thomas - 1991
6231	Maximum likelihood from incomplete data via the EM algorithm - Dempster, Laird, et al. - 1977
3909	Neural Networks for Pattern Recognition - Bishop - 1995
3340	Pattern Classification and Scene Analysis - Duda, Hart - 1973
3143	Classification and Regression Trees - Breiman, Friedman, et al. - 1983
2715	Neural networks: A comprehensive foundation (2nd ed.). Upper Saddle River - Haykin - 1999
1300	Vector Quantization and Signal Compression - Gersho, Gray - 1991
1105	Information theory and reliable communication - Gallager - 1968
910	Spatial interaction and the statistical analysis of lattice systems - Besag - 1974
887	Bayesian Data Analysis - Gelman, Carlin, et al. - 2004
801	A probabilistic theory of pattern recognition - Devroye, Györfi, et al. - 1996
665	Adaptive mixtures of local experts - Jacobs, Jordan, et al. - 1991
531	Pattern Recognition: A statistical approach - PA, Kittler - 1982
526	Textures: A Photographic Album for Artists and Designers - Brodatz - 1966
331	Pyramid-based texture analysis/synthesis - Heeger, Bergen - 1995
238	Rate Distortion Theory: A mathematical basis for data compression. Englewood Cliffs (New - Berger - 1971
183	Digital Coding of Waveforms: Principles and Applications to Speech and Video; Prentice-Hall - Jayant, Noll - 1984
176	Minimum complexity density estimation - Barron, Cover - 1991
170	An introduction to arithmetic coding - Langdon - 1984
164	Finite Mixture Distributions - Everitt, Hand - 1981
162	Signal compression based on models of human perception - Jayant, Johnston, et al. - 1993
129	Computation of channel capacity and rate-distortion function - Blahut - 1972
114	Real analysis and probability - Ash - 1972
113	Resource Allocation Problems - Algorithmic Approaches - Ibaraki, Katoh - 1988
105	Optimal pruning with application to treestructured source coding and modeling - Chou, Lookabaugh, et al. - 1989
84	Asymptotically efficient quantizing - Gish, Pierce - 1968
71	Block quantization of correlated gaussian random variables - Huang, Schultheiss - 1963
65	Universal noiseless coding - Davisson - 1980
61	Optimal partitioning for classification and regression trees - Chou - 1991
60	Spectra of quantized signals - Bennett - 1948
51	Projection pursuit density estimation - Friedman, H, et al. - 1984
49	personal communication - Persons, Brown
47	Vector quantization of image sub bands: A survey - Cosman, Gray, et al. - 1996
47	Present position and potential developments: Some personal views, statistical theory, the prequential approach - Dawid - 1984
47	Compression of Black-White Images with Arithmetic Coding - Langdon - 1981
45	The use of Markov random fields as models of texture - Hassner, Sklansky - 1980
41	Theories of Probability: An Examination of Foundations - Fine - 1973
38	Kernel Discriminant Analysis - Hand - 1982
34	Multidimensional asymptotic quantization theory with rth power distortion measures - Bucklew, Wise - 1982
32	Nonparametric Density Estimation: The L 1 View - Devroye, Gyorfi - 1985
30	Least squares quantization - Lloyd
24	Projection pursuit. The Annals of Statistics - Huber - 1985
21	Progressive wavelet image coding based on a conditional probability model - Buccigrossi, Simoncelli - 1997
21	Information rates of autoregressive processes - Gray - 1970
14	Characterization and Estimation of Two-Dimensional ARMA Models - Kashyap - 1984
12	der Meulen, “Distribution estimation consistent in total variation and in two types of information divergence - Barron, Györfi, et al. - 1454
12	Minimum entropy quantizers and permutation codes - Berger - 1982
12	Weighted universal image compression - Effros, Chou, et al.
10	The Metaphysical Foundations of Modern Physical Science - Burtt - 1980
7	Conditional entropy-constrained vector quantization of linear predictive coefficients - Chou, Lookabaugh - 1990