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1 November 1990 Maximum entropy image reconstruction from projections via Lagrange parameter analysis
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A method for maximum-entropy image reconstruction from projections is presented. Two image entropies are studied under the assumption that image-density distributions over image-element array follow a multinomial random process. The multinomial distribution process reflects those physical aspects of images: (1) image density is non-negative, (2) image-density distributions are conserved, (3) image-density distributions are spatially correlated. One image entropy assumes a uniform spatial correlation and resembles Shannon's entropy that has been widely used in image-processing problems. The other assumes non-uniform spatial correlations among nearby image elements and resembles the cross entropy introduced by Kuilback and Leibler. The non-uniform correlations among nearby elements are modeled in a similar manner as Markov random field does, i.e., image density changes slowly within a homogeneous region and rapidly at the boundaries of the homogeneous regions. The projections are assumed as measured by a linear imaging system. The measurement constraints are incorporated into the maximum-entropy method by employing a set of Lagrange parameters. Each Lagrange parameter is related to a constraint of a datum. The solutions that maximize the image entropies subject to the measurement constraints are given, as determined respectively by a superposition of the Lagrange parameters. The Lagrange parameters are then estimated iteratively using a steepest descent technique. Comparative study on the image entropies is carried out using computer generated noise-free and noisy projections. Improved results are obtained by use of the image entropy assuming the non-uniform correlations. The non-uniform correlated image entropy needs little more computation time and memory.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Zhengrong Liang "Maximum entropy image reconstruction from projections via Lagrange parameter analysis", Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990);

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