论文标题
在Lipschitz般的凸状条件下重新访问线性化的Bregman迭代
Revisiting Linearized Bregman Iterations under Lipschitz-like Convexity Condition
论文作者
论文摘要
线性化的Bregman迭代（LBREI）及其变体在信号/图像处理和压缩传感方面受到了极大的关注。最近，LBREI已扩展到较大的非凸功能，以及剩下的几个理论问题以进行进一步研究。特别是，Lipschitz的梯度连续性假设排除了其在许多实际应用中的使用。在这项研究中，我们提出了一个广义算法框架来统一LBREI型方法。我们的主要发现是，在凸和非convex情况下，梯度Lipschitz的连续性假设都可以被Lipschitz样的凸状条件取代。然后将所提出的框架和理论应用于线性/二次逆问题。
The linearized Bregman iterations (LBreI) and its variants have received considerable attention in signal/image processing and compressed sensing. Recently, LBreI has been extended to a larger class of nonconvex functions, along with several theoretical issues left for further investigation. In particular, the gradient Lipschitz continuity assumption precludes its use in many practical applications. In this study, we propose a generalized algorithmic framework to unify LBreI-type methods. Our main discovery is that the gradient Lipschitz continuity assumption can be replaced by a Lipschitz-like convexity condition in both convex and nonconvex cases. The proposed framework and theory are then applied to linear/quadratic inverse problems.
