Superiorization: an optimization heuristic for medical physics.

Area of Science:

• Optimization methodologies
• Medical physics applications
• Heuristic algorithms

Background:

• Constrained optimization problems are prevalent in medical physics.
• Existing iterative algorithms may not always yield optimal solutions according to specific criteria.
• The need for adaptable optimization techniques that respect physical constraints is critical.

Purpose of the Study:

• To mathematically validate and describe the superiorization methodology, a heuristic optimization approach.
• To explore its applicability to medical physics problems with defined constraints and optimization criteria.
• To demonstrate its potential for generating solutions that are both constraint-compatible and optimized.

Main Methods:

• The superiorization methodology is presented as a heuristic solver for constrained optimization.
• It leverages the perturbation resilience of iterative algorithms to steer solutions towards an optimization criterion.
• The approach is general and applicable to various iterative procedures and optimization criteria in medical physics.

Main Results:

• A procedure is presented for automatically generating a 'superiorized' version of any iterative algorithm.
• The superiorized algorithm guarantees constraint compatibility while improving the solution based on the optimization criterion.
• Demonstrated effectiveness on simulated computerized tomography data, showing competitiveness with specialized algorithms.

Conclusions:

• Superiorization has a broad applicability to constrained optimization problems.
• Its key advantage is the automatic generation of superiorization algorithms from existing constraint-compatible ones.
• It offers an efficient pathway to practical solutions for complex optimization problems in medical physics.