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Phys Med Biol. 2006 May 21;51(10):2353-65. Epub 2006 Apr 26.

A unified approach for inversion problems in intensity-modulated radiation therapy.

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  • 1Department of Mathematics, University of Haifa, Mt Carmel, Haifa 31905, Israel.


We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

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