The present paper focuses on accelerating monotone fast iterative shrinkage–thresholding algorithm (MFISTA) that is popular to solve the basis pursuit denoising problem for sparse recovery. Inspired by a recent work that accelerates MFISTA with line search, we alternatively use a much more effective speed-up option, termed sequential subspace optimization. Furthermore, instead of manually setting the number of previous propagation directions in the subspace beforehand, we propose an adaptive method to set it. Additionally, for approximating the absolute value function, we analyze the superiority of a smooth version used in this paper over the one recommended in a previous work, and give an analytical closed-form expression for the shrinkage operator corresponding to the smooth approximation. The experiments presented here show that the proposed method achieves faster convergence speeds in terms of iteration and run-time.

中文翻译：

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用于稀疏恢复的具有顺序子空间优化的加速单调快速迭代收缩阈值算法

本论文侧重于加速单调快速迭代收缩-阈值算法（MFISTA），该算法流行用于解决稀疏恢复的基础追踪去噪问题。受最近一项通过线搜索加速 MFISTA 的工作的启发，我们或者使用更有效的加速选项，称为顺序子空间优化。此外，我们不是事先手动设置子空间中先前传播方向的数量，而是提出了一种自适应方法来设置它。此外，为了逼近绝对值函数，我们分析了本文中使用的平滑版本相对于先前工作中推荐的版本的优越性，并给出了与平滑逼近相对应的收缩算子的解析闭式表达式。