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Penalty functions or regularization terms that promote structured solutionsto optimization problems are of great interest in many fields. Proposed in thiswork is a nonconvex structured sparsity penalty that promotes one-sparsitywithin arbitrary overlapping groups in a vector. This allows one to enforcemutual exclusivity between components within solutions to optimizationproblems. We show multiple example use cases (including a total variationvariant), demonstrate synergy between it and other regularizers, and propose analgorithm to efficiently solve problems regularized or constrained by theproposed penalty.

SWAGGER: Sparsity Within and Across Groups for General Estimation and Recovery