标题： 具有中位数绝对偏差的自适应迭代软阈值算法 显示英文标题

标题： Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation

摘要： 自适应迭代软阈值算法（ISTA）已成为一种流行的算法，用于在不显式调整正则化参数$\lambda$的情况下找到LASSO问题的满意解。 尽管自适应ISTA是一个成功的实用算法，但很少有理论结果存在。 在本文中，我们提出了对自适应ISTA的理论分析，该算法采用通过中位数绝对偏差估计噪声水平的阈值策略。 我们展示了算法的固定点的性质，包括尺度等变性、非唯一性和局部稳定性，证明了局部线性收敛保证，并展示了其全局收敛行为。 显示英文摘要

摘要： The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is a successful practical algorithm, few theoretical results exist. In this paper, we present the theoretical analysis on the adaptive ISTA with the thresholding strategy of estimating noise level by median absolute deviation. We show properties of the fixed points of the algorithm, including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior.