The Matrix Orthogonal Decomposition Problem in Intensity-Modulated Radiation Therapy

  • Xin Dou
  • Xiaodong Wu
  • John E. Bayouth
  • John M. Buatti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


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.


Directed Edge Decomposition Problem Base Vertex Vertical Complexity Total Edge Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xin Dou
    • 1
  • Xiaodong Wu
    • 1
    • 2
  • John E. Bayouth
    • 2
  • John M. Buatti
    • 2
  1. 1.Dept. of Electrical and Computer EngineeringUniversity of IowaIowa CityUSA
  2. 2.Dept. of Radiation OncologyUniversity of IowaIowa CityUSA

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