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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Dou, X., Wu, X., Bayouth, J. E., & Buatti, J. M. (2006). The matrix orthogonal decomposition problem in intensity-modulated radiation therapy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 156–165). Springer Verlag. https://doi.org/10.1007/11809678_18
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