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

TLDR

The authors propose a unified model that integrates dose constraints and radiation source constraints within a split feasibility framework. The model minimizes a weighted proximity function of squared distances to constraint sets, ensuring convergence to a feasible point when the split feasibility problem is consistent, or to a minimally violating solution otherwise. Computational experiments confirm the model’s validity and the effectiveness of the proposed algorithmic scheme.

Abstract

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.