MEGS: A Penalty for Mutually Exclusive Group Sparsity
MEGS: A Penalty for Mutually Exclusive Group Sparsity
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DOI：
10.1109/ojsp.2023.3271249
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发表时间：
2023
影响因子：
2.8
通讯作者：
Charles Saunders;V. K. Goyal
中科院分区：
文献类型：
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作者：
Charles Saunders;V. K. Goyal
罚函数或正则化项，促进结构化的解决方案，优化问题是在许多领域的极大兴趣。我们引入MEGS，一个非凸的结构稀疏惩罚，促进组件之间的相互排他性的解决方案，优化问题。这在向量中的任意重叠组内强制或促进1-稀疏性。互斥结构由矩阵${\bf {S}}$表示。我们从工程原理讨论${\bf {S}}$的设计，并展示示例用例，包括3D成像中的遮挡建模和图像恢复中使用的总变差变体。我们还展示了MEGS和其他正则化器之间的协同作用，并提出了一种算法来有效地解决问题的正则化或约束MEGS。
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 ${\bf {S}}$. We discuss the design of ${\bf {S}}$ 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.