The superiorization methodology is very general and has been used successfully in many important practical applications, such as iterative reconstruction of images from their projections,[1][2][3] single-photon emission computed tomography,[4] radiation therapy[5][6][7] and nondestructive testing,[8] just to name a few.
A special issue of the journal Inverse Problems[9] is devoted to superiorization, both theory[10][11][12] and applications.
[3][6][7] An important case of superiorization is when the original algorithm is "feasibility-seeking" (in the sense that it strives to find some point in a feasible region that is compatible with a family of constraints) and the perturbations that are introduced into the original iterative algorithm aim at reducing (not necessarily minimizing) a given merit function.
Such is, for example, the class of projected gradient methods wherein the unconstrained minimization inner step "leads" the process and a projection onto the whole constraints set (the feasible region) is performed after each minimization step in order to regain feasibility.
[17] SNARK14[18] is a software package for the reconstruction if 2D images from 1D projections that has a built-in capability of superiorizing any iterative algorithm for any merit function.