Nonconvex penalties with analytical solutions for one-bit compressive sensing
Nonconvex penalties with analytical solutions for one-bit compressive sensing
复制标题
一位压缩传感的非凸惩罚与解析解
DOI：
10.1016/j.sigpro.2017.10.023
复制
发表时间：
2018
影响因子：
4.4
通讯作者：
Yan Ming
中科院分区：
文献类型：
--
作者：
Huang Xiaolin;Yan Ming
One-bit measurements widely exist in the real world and can be used to recover sparse signals. This task is known as one-bit compressive sensing (1bit-CS). In this paper, we propose novel algorithms based on both convex and non-convex sparsity-inducing penalties for robust 1bit-CS. We consider the dual problem, which has only one variable and provides a sufficient condition to verify whether a solution is globally optimal or not. For positive homogeneous penalties, a globally optimal solution can be obtained in two steps: a proximal operator and a normalization step. For other penalties, we solve the dual problem, and it needs to evaluate the proximal operators for many times. Then we provide fast algorithms for finding analytical solutions for three penalties: minimax concave penalty (MCP), ℓ0norm, and sorted ℓ1penalty. Specifically, our algorithm is more than 200 times faster than the existing algorithm for MCP. Its efficiency is comparable to the algorithm for the ℓ1penalty in time, while its performance is much better than ℓ1. Among these penalties, sorted ℓ1is most robust to noise in different settings.
