MEGS: A Penalty for Mutually Exclusive Group Sparsity

• Main Authors: Goyal, V.K (Author), Saunders, C. (Author)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers Inc. 2023
• Subjects: Behavioral sciences; group sparsity; Imaging; inverse problems; Optimization; regularization; Signal processing; Signal processing algorithms; Solid modeling; sparsity; structured sparsity; Three-dimensional displays
• Online Access: View Fulltext in Publisher; View in Scopus
• Physical Description: 9
• ISBN: 26441322 (ISSN)
• DOI: 10.1109/OJSP.2023.3271249

Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. We introduce MEGS, a nonconvex structured sparsity penalty that promotes mutual exclusivity between components in solutions to optimization problems. This enforces, or promotes, 1-sparsity within arbitrary overlapping groups in a vector. The mutual exclusivity structure is represented by a matrix S. We discuss the design of S from engineering principles and show example use cases including the modeling of occlusions in 3D imaging and a total variation variant with uses in image restoration. We also demonstrate synergy between MEGS and other regularizers and propose an algorithm to efficiently solve problems regularized or constrained by MEGS. Author