DocumentCode :
792412
Title :
Adaptive wavelet graph model for Bayesian tomographic reconstruction
Author :
Frese, Thomas ; Bouman, Charles A. ; Sauer, Ken
Author_Institution :
McKinsey & Co., Chicago, IL, USA
Volume :
11
Issue :
7
fYear :
2002
fDate :
7/1/2002 12:00:00 AM
Firstpage :
756
Lastpage :
770
Abstract :
We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.
Keywords :
Bayes methods; Gaussian distribution; emission tomography; image reconstruction; image resolution; iterative methods; medical image processing; optimisation; trees (mathematics); wavelet transforms; Bayesian tomographic reconstruction; Haar basis; adaptive wavelet graph model; coarse scale data; coarse scale information; coarse-to-fine scale dependencies; computationally efficient algorithm; conditional distribution; emission tomography; graph dependency structure; iterative Bayesian space domain optimization; multiresolution image reconstruction; nonlinear adaptation mechanism; nonlinear classification; nonlocal observations; overlapping windows; pixel positivity constraints; reconstruction quality; scale recursive updates; scaling coefficients; space domain formulation; spatially nonhomogeneous Gaussian distribution; training images; transmission tomography; wavelet bases; wavelet coefficients; wavelet tree; Bayesian methods; Gaussian distribution; Image reconstruction; Image resolution; Iterative algorithms; Spatial resolution; Tomography; Tree graphs; Wavelet coefficients; Wavelet domain;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2002.801586
Filename :
1021082
Link To Document :
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