Abstract
In this paper, we study an interesting matrix decomposition problem that seeks to decompose a “complicated” matrix into two “simpler” matrices while minimizing the sum of the horizontal complexity of the first sub-matrix and the vertical complexity of the second sub-matrix. The matrix decomposition problem is crucial for improving the “step-and-shoot” delivery efficiency in Intensity-Modulated Radiation Therapy, which aims to deliver a highly conformal radiation dose to a target tumor while sparing the surrounding normal tissues. Our algorithm is based on a non-trivial graph construction scheme, which enables us to formulate the decomposition problem as computing a minimum s-t cut in a 3-D geometric multi-pillar graph. Experiments on randomly generated intensity map matrices and on clinical data demonstrated the efficiency of our algorithm.
This research was supported in part by a faculty start-up fund from the University of Iowa, and in part by a fund from the American Cancer Society through an Institutional Research Grant to the Holden Comprehensive Cancer Center, the University of Iowa, Iowa City, IA, USA.
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Dou, X., Wu, X., Bayouth, J.E., Buatti, J.M. (2006). The Matrix Orthogonal Decomposition Problem in Intensity-Modulated Radiation Therapy. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_18
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DOI: https://doi.org/10.1007/11809678_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36925-7
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