Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization
Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization
复制标题
使用广义非凸正则化有效稳健地恢复稀疏信号和图像
DOI：
10.1109/tci.2017.2744626
复制
发表时间：
2017-12-01
影响因子：
5.4
通讯作者：
Liu, Peilin
中科院分区：
文献类型：
--
作者：
Wen, Fei;Pei, Ling;Liu, Peilin
本文讨论了从压缩的测量稀疏信号的鲁棒重建问题。我们提出了一个强大的制定稀疏重建，采用l（1）-范数作为损失函数的残余误差，并利用广义非凸惩罚稀疏诱导。l（1）-损失比流行的l（2）-损失对测量中的异常值不太敏感，而非凸惩罚具有改善流行的凸LASSO惩罚的偏差问题的能力，因此可以产生更准确的恢复。为了有效地解决这个非凸和非光滑的最小化配方，我们提出了一个一阶算法的交替方向的乘子方法的基础上。在推导新算法时采用了对l（1）-损失函数的光滑化策略，使算法收敛。进一步，对广义非凸正则化，给出了新算法收敛的一个充分条件。数值实验结果表明，该算法在恢复稀疏信号和可压缩图像方面比现有算法有更好的性能。新算法的规模以及大规模的问题，经常遇到的图像处理。
This paper addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction that employs the l(1)-norm as the loss function for the residual error and utilizes a generalized nonconvex penalty for sparsity inducing. The l(1)-loss is less sensitive to outliers in the measurements than the popular l(2)-loss, while the nonconvex penalty has the capability of ameliorating the bias problem of the popular convex LASSO penalty and thus can yield more accurate recovery. To solve this nonconvex and nonsmooth minimization formulation efficiently, we propose a first-order algorithm based on alternating direction method of multipliers. A smoothing strategy on the l(1)-loss function has been used in deriving the new algorithm to make it convergent. Further, a sufficient condition for the convergence of the new algorithm has been provided for generalized nonconvex regularization. In comparison with several state-of-the-art algorithms, the new algorithm showed better performance in numerical experiments in recovering sparse signals and compressible images. The new algorithm scales well for large-scale problems, as often encountered in image processing.