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26 October 1999 Multiscale models for Bayesian inverse problems
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In this paper we introduce a Bayesian tomographic reconstruction technique employing a wavelet-based multiresolution prior model. While the image is modeled in the wavelet-domain, the actual tomographic reconstruction is performed in a fixed resolution pixel domain. In comparison to performing the reconstruction in the wavelet domain, the pixel based optimization facilitates enforcement of the positivity constraint and preserves the sparseness of the tomographic projection matrix. Thus our technique combines the advantages of multiresolution image modeling with those of performing the constrained optimization in the pixel domain. In addition to this reconstruction framework, we introduce a novel multiresolution prior model. This prior model attempts to capture the dependencies of wavelet coefficients across scales by using a Markov chain structure. Specifically, the model employs nonlinear predictors to locally estimate the prior distribution of wavelet coefficients from coarse scale information. We incorporate this prior into a coarse-to-fine scale tomographic reconstruction algorithm. Preliminary results indicate that this algorithm can potentially improve reconstruction quality over fix resolution Bayesian methods.
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Thomas Frese, Charles A. Bouman, and Ken D. Sauer "Multiscale models for Bayesian inverse problems", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999);

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