Minimizing Total Variation for Field Splitting with Feathering in Intensity-Modulated Radiation Therapy
In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multileaf collimator (MLC) with a maximum leaf spread constraint is used to deliver the prescribed radiation intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large IM into several overlapping sub-IMs with each being delivered separately. We develop an efficient algorithm for solving the field splitting problem while minimizing the total variation of the resulting sub-IMs, thus improving the treatment delivery efficiency. Our basic idea is to formulate the field splitting problem as computing a shortest path in a directed acyclic graph, which expresses a special “layered” structure. The edge weights in the graph can be computed by solving an optimal vector decomposition problem using local searching and the proximity scaling technique as we can prove the L\(^\natural\)-convexity and totally unimodularity of the problem. Moreover, the edge weights of the graph satisfy the Monge property, which enables us to solve this shortest path problem by examining only a small portion of the graph, yielding a time-efficient algorithm.
KeywordsShort Path Directed Acyclic Graph Edge Weight Short Path Problem Integer Programming Problem
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