Properties of an algorithm for solving the inverse problem in radiation therapy

Abstract

An iterative method for solving the inverse problem in radiation therapy is presented and the corresponding problem of minimising a functional on Rn to R1 is formulated. The appealing properties of the algorithm are that under-dosage is avoided and the physical constraints of non-negativity, which are particular to radiation therapy, are accurately incorporated. It is shown that the solution generated by the algorithm is the closest possible dose distribution to the desired dose distribution under these constraints. The linear convergence of the rather crude gradient method with fixed-step length is compensated by the fact that fast Fourier transform techniques can be used to speed up the calculations. The algorithm is applied to numerical examples and compared with a similar algorithm generating a strict minimisation according to the least-squares norm.