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The selection of beam orientations, which is a key step in radiationtreatment planning, is particularly challenging for non-coplanar radiotherapysystems due to the large number of candidate beams. In this paper, we reportprogress on the group sparsity approach to beam orientation optimization,wherein beam angles are selected by solving a large scale fluence mapoptimization problem with an additional group sparsity penalty term thatencourages most candidate beams to be inactive. The optimization problem issolved using an accelerated proximal gradient method, the Fast IterativeShrinkage-Thresholding Algorithm (FISTA). We derive a closed-form expressionfor a relevant proximal operator which enables the application of FISTA. Theproposed algorithm is used to create non-coplanar treatment plans for fourcases (including head and neck, lung, and prostate cases), and the resultingplans are compared with clinical plans. The dosimetric quality of the groupsparsity treatment plans is superior to that of the clinical plans. Moreover,the runtime for the group sparsity approach is typically about 5 minutes.Problems of this size could not be handled using the previous group sparsitymethod for beam orientation optimization, which was slow to solve much smallercoplanar cases. This work demonstrates for the first time that the groupsparsity approach, when combined with an accelerated proximal gradient methodsuch as FISTA, works effectively for non-coplanar cases with 500-800 candidatebeams.

Fast non-coplanar beam orientation optimization based on group sparsity