## Abstract

Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the Expectation-Maximization algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of real-world images. In the image HMT (iHMT) model we use the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to just nine easily trained parameters (independent of the size of the image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms all other wavelet-based estimators in the current literature, both in mean-square error and visual metrics.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Publisher | Society of Photo-Optical Instrumentation Engineers |

Pages | 31-44 |

Number of pages | 14 |

Volume | 3816 |

State | Published - 1999 |

Event | Proceedings of the 1999 Mathematical Modeling, Bayesian Estimation, and Inverse Problems - Denver, CO, USA Duration: Jul 21 1999 → Jul 23 1999 |

### Other

Other | Proceedings of the 1999 Mathematical Modeling, Bayesian Estimation, and Inverse Problems |
---|---|

City | Denver, CO, USA |

Period | 7/21/99 → 7/23/99 |

## ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics