Bayesian image reconstruction from Fourier-domain samples using prior edge information: convergence and parameter sensitivity

Thomas S. Denney Jr.; Stanley J. Reeves

doi:10.1117/12.641706

2 February 2006 Bayesian image reconstruction from Fourier-domain samples using prior edge information: convergence and parameter sensitivity

Thomas S. Denney Jr., Stanley J. Reeves

Author Affiliations +

Proceedings Volume 6065, Computational Imaging IV; 60650E (2006) https://doi.org/10.1117/12.641706
Event: Electronic Imaging 2006, 2006, San Jose, California, United States

Abstract

Image reconstruction from Fourier-domain measurements is a specialized problem within the general area of image reconstruction using prior information. The structure of the equations in Fourier imaging is challenging, since the observation equation matrix is non-sparse in the spatial domain but diagonal in the Fourier domain. Recently, the Bayesian image reconstruction with prior edges (BIRPE) algorithm has been proposed for image reconstruction from Fourier-domain samples using edge information automatically extracted from a high-resolution prior image. In the BIRPE algorithm, the maximum a posteriori (MAP) estimate of the reconstructed image and edge variables involves high-dimensional, non-convex optimization, which can be computationally prohibitive. The BIRPE algorithm performs this optimization by iteratively updating the estimate of the image then updating the estimate of the edge variables. In this paper, we propose two techniques for updating the image based on fixed edge variables one based on iterated conditional modes (ICM) and the other based on Jacobi iteration. ICM is guaranteed to converge, but, depending on the structure of the Fourier-domain samples, can be computationally prohibitive. The Jacobi iteration technique is more computationally efficient but does not always converge. In this paper, we study the convergence properties of the Jacobi iteration technique and its parameter sensitivity.

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Thomas S. Denney Jr. and Stanley J. Reeves "Bayesian image reconstruction from Fourier-domain samples using prior edge information: convergence and parameter sensitivity", Proc. SPIE 6065, Computational Imaging IV, 60650E (2 February 2006); https://doi.org/10.1117/12.641706

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KEYWORDS

Reconstruction algorithms

Image restoration

Signal to noise ratio

Image segmentation

Optimization (mathematics)

Algorithm development

Image analysis

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