非凸稀疏诱导多罚正则化的计算方法
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization
摘要：
在这项工作中，我们考虑的数值效率和收敛速度的求解器的非凸多罚公式重建稀疏信号时，从嘈杂的线性测量。我们扩展了现有的方法，减少到一个增广的单罚制定的基础上，非凸设置，并讨论其在大规模应用中的计算棘手性。为了规避这一限制，我们提出了一种替代的基于无穷卷积的单罚减少，该方法具有增强方法的优点，但在计算上对问题大小的依赖性较小。我们提供的线性收敛速度，这两种方法，以及它们对设计参数的依赖。数值实验证实了我们的理论发现。
英文摘要：
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction to an augmented single-penalty formulation, to the non-convex setting and discuss its computational intractability in large-scale applications. To circumvent this limitation, we propose an alternative single-penalty reduction based on infimal convolution that shares the benefits of the augmented approach but is computationally less dependent on the problem size. We provide linear convergence rates for both approaches, and their dependence on design parameters. Numerical experiments substantiate our theoretical findings.
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