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

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.

Solve the split equality problem by a projection algorithm with inertial effects

“…Many problems in mathematics and other sciences can be regarded as a split equality problem, such as the variational form of a PDE's in domain decomposition for PDE's [3], the agents who interplay only via some components of their decision variables in decision [2] and the weak coupling between the vector of doses absorbed in all voxels and that of the radiation intensity in the (IMRT) [7].…”

Convergence analysis of a Halpern-like iterative algorithm in Hilbert spaces

“…It has been found that the split feasibility problem can also be used in various disciplines such as image restoration, computer tomograph and radiation therapy treatment planning [4,5,7].…”

Strong convergence theorems for a nonexpansive mapping and its applications for solving the split feasibility problem

“…As we know, the SFP has received so much attention due to its applications in intensity-modulated radiation therapy, signal processing, and image reconstruction, see Byrne [1,2], Censor [4][5][6], Ceng [3], Fan et al [7], Xu [20,21], Kraikaew and Saejung [9], Moudafi [10], Qu et al [12][13][14], Qin and Yao [11], Yang et al [16,22,27,28], Yao et al [23][24][25][26], and so on.…”