29 July 1993 ART with optimal 2D sampling function
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Abstract
A new model is proposed to reconstruct an image from its ray sum using Algebraic Reconstruction Techniques (ART). Assuming that the original image is band limited, an iterative algorithm is developed that evaluates the updated image and reduces the sampling error during each iteration. Depending on a weight factor, estimation of the updated images in each iteration is the contribution of correction to each sample of the ray sum. The weight factor is the fractional area intercepted by the ray sum and the sampling function. To model a 2D image, an optimal sampling function is used where the sampling function is a cylindrical pulse instead of the customary flat-top sample version of a 2D square pulse. Given energy concentration of the pulse, a class of such pulses are generated. A pulse with maximum concentration of energy is used for sampling of the 2D image. By determining the eigenfunctions of a homogeneous Fredholm equation of the second kind with a symmetric kernel such a pulse is generated. Moreover, it is shown that eigenfunctions of the above integral equation are those classes of pulses where the corresponding eigenvalue is the measure of the concentration of an eigenfunction. The desired pulse is an eigenfunction with the maximum eigenvalue.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Babak Farsaii, Babak Farsaii, } "ART with optimal 2D sampling function", Proc. SPIE 1905, Biomedical Image Processing and Biomedical Visualization, (29 July 1993); doi: 10.1117/12.148613; https://doi.org/10.1117/12.148613
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