论文标题
$ l_0 $ norm正规化最小在问题的同质坐标坐标下降优化方法
A Homotopy Coordinate Descent Optimization Method for $l_0$-Norm Regularized Least Square Problem
论文作者
论文摘要
本文提出了一种均匀坐标下降（HCD）方法，以解决压缩感应的$ l_0 $ norm正规化最小平方（$ L_0 $ -LS）问题，该问题将同型技术与坐标下降方法的变体结合在一起。与经典的坐标下降算法不同，HCD提供了三种策略来加快收敛性：温暖的开始初始化，主动设置更新和强有力的主动设置初始化规则。使用强规则会预选该活动集，然后在不变集合的情况下更新活动集的坐标。同型策略为一系列降低正则化因子值的序列提供了一组温暖的开始解决方案，从而确保沿同置溶液沿线路径的所有迭代稀疏。对模拟信号和自然信号的计算实验证明了所提出的算法的有效性，在准确有效地重建$ L_0 $ -LS问题的稀疏解，无论观察是否嘈杂。
This paper proposes a homotopy coordinate descent (HCD) method to solve the $l_0$-norm regularized least square ($l_0$-LS) problem for compressed sensing, which combine the homotopy technique with a variant of coordinate descent method. Differs from the classical coordinate descent algorithms, HCD provides three strategies to speed up the convergence: warm start initialization, active set updating, and strong rule for active set initialization. The active set is pre-selected using a strong rule, then the coordinates of the active set are updated while those of inactive set are unchanged. The homotopy strategy provides a set of warm start initial solutions for a sequence of decreasing values of the regularization factor, which ensures all iterations along the homotopy solution path are sparse. Computational experiments on simulate signals and natural signals demonstrate effectiveness of the proposed algorithm, in accurately and efficiently reconstructing sparse solutions of the $l_0$-LS problem, whether the observation is noisy or not.
