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We propose algorithms and software for computing projections onto theintersection of multiple convex and non-convex constraint sets. The softwarepackage, called SetIntersectionProjection, is intended for the regularizationof inverse problems in physical parameter estimation and image processing. Theprimary design criterion is working with multiple sets, which allows us tosolve inverse problems with multiple pieces of prior knowledge. Our algorithmsoutperform the well known Dykstra's algorithm when individual sets are not easyto project onto because we exploit similarities between constraint sets. Otherdesign choices that make the software fast and practical to use, includerecently developed automatic selection methods for auxiliary algorithmparameters, fine and coarse grained parallelism, and a multilevel accelerationscheme. We provide implementation details and examples that show how thesoftware can be used to regularize inverse problems. Results show that webenefit from working with all available prior information and are not limitedto one or two regularizers because of algorithmic, computational, orhyper-parameter selection issues.

Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems