  The selection of beam orientations, which is a key step in radiation
treatment planning, is particularly challenging for non-coplanar radiotherapy
systems due to the large number of candidate beams. In this paper, we report
progress on the group sparsity approach to beam orientation optimization,
wherein beam angles are selected by solving a large scale fluence map
optimization problem with an additional group sparsity penalty term that
encourages most candidate beams to be inactive. The optimization problem is
solved using an accelerated proximal gradient method, the Fast Iterative
Shrinkage-Thresholding Algorithm (FISTA). We derive a closed-form expression
for a relevant proximal operator which enables the application of FISTA. The
proposed algorithm is used to create non-coplanar treatment plans for four
cases (including head and neck, lung, and prostate cases), and the resulting
plans are compared with clinical plans. The dosimetric quality of the group
sparsity 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 sparsity
method for beam orientation optimization, which was slow to solve much smaller
coplanar cases. This work demonstrates for the first time that the group
sparsity approach, when combined with an accelerated proximal gradient method
such as FISTA, works effectively for non-coplanar cases with 500-800 candidate
beams.
