The superiorization method (SM) is situated between feasibility-seeking and constrained
optimization. Instead of aiming at the minimum of a given objective function
over a constraint set, it seeks a feasible point at which the objective function
value is reduced — though not necessarily minimal — compared to that reached by
the feasibility-seeking algorithm alone. This can be advantageous for problems in
which the constraints may be inconsistent, in which secondary goals such as noise
reduction or regularization describe soft preferences rather than hard targets, or in
which a mathematically optimal solution is not strictly required. While the method
has been investigated for several applications in physics, its broader use has been
limited, in part due to the lack of openly available software for researchers wishing
to explore it.
In this work we apply superiorization to three problems from applied physics:
seismic image reconstruction, low-dose CT reconstruction and intensity-modulated
radiotherapy treatment planning. These experiments are conducted with SupPy, an
open-source modularized Python toolbox developed for this work, which supports
execution of feasibility-seeking algorithms and their superiorized version on both the
CPU and the GPU. In all three cases the superiorized algorithms achieve favorable
results compared to feasibility-seeking alone, with reduced noise in the imaging examples
and lowered body dose in the radiotherapy plans. For the radiotherapy case
we further observe that superiorization produces clinically viable plans on infeasible
constraint sets.