Optimal binary coding matrices for multiplexed x-ray imaging

David S. Lalush

doi:10.1117/12.811124

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12 March 2009 Optimal binary coding matrices for multiplexed x-ray imaging

David S. Lalush

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Proceedings Volume 7258, Medical Imaging 2009: Physics of Medical Imaging; 72581S (2009) https://doi.org/10.1117/12.811124
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

Abstract

We study a class of binary matrices with excellent noise properties for controlling multiplexing patterns in a multiple-source, single-detector X-ray system. For such a system, turning multiple sources on at a time in a prescribed pattern (multiplexing), can offer noise advantages under certain conditions. The patterns used can be represented by binary matrices which determine the noise properties of the decoded images. Hadamard S-matrices have long been used in spectroscopy, but they are optimal only in systems with little photonic noise. In X-ray systems with energy-integrating detectors, the noise structure may be a mix of constant (electronic) noise and noise proportional to the signal (photonic noise). Under mixed noise conditions, we demonstrate that a certain class of balanced incomplete block design (BIBD) matrices offers better noise performance over a wider range of noise mixes than the Hadamard matrices. Symmetric BIBD matrices are characterized by three parameters: v = the number of sources in the multiplexing array; k = the number of sources on at a time; and λ = the number of multiplexed frames shared by any pair of sources. We compare noise performance in decoded images for several families of BIBD matrices and show that the BIBD matrices with λ = 1 offer the best performance. We also offer insight into how the available matrices affect parameters of system design in a multiplexing X-ray system. We conclude that the BIBD(v,k,λ = 1) matrices or matrices derived from them are the best choices for multiplexing in multi-source X-ray systems.

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David S. Lalush "Optimal binary coding matrices for multiplexed x-ray imaging", Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72581S (12 March 2009); https://doi.org/10.1117/12.811124

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