...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Signal processing >Nonconvex penalties with analytical solutions for one-bit compressive sensing
【24h】

Nonconvex penalties with analytical solutions for one-bit compressive sensing

机译：具有一比特压缩感测的解析解的非凸罚分

获取原文
获取原文并翻译 | 示例
   

获取外文期刊封面封底 >>

       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Highlights•We analyze a generic model for 1bit-CS and provide a sufficient condition for the global optimality.•For positive homogeneous penalties, we show that the optimal solution can be obtained by two steps: a proximal operator and normalization step. For general penalty, we provide a generic algorithm by solving the dual problem.•We provide algorithms for finding analytical solutions for several non-convex penalties including MCP, ℓ0norm, and the sorted ℓ1penalty.•These analytical solution make the algorithms much faster than existing 1bit-CS the algorithms much faster than existing 1bit-CS the algorithms for non-convex penalties and even comparable to that the convex ℓ1minimization problem.•These analytical solution enable people to analyze theoretical properties such as sampling complexity for non-convex penalties, which is beyond the focus of this paper. beyond the focus of this paper.AbstractOne-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.
机译： 突出显示 • 我们分析了1bit-CS的通用模型，并为全局最优性提供了充分条件。 < ce：list-item id =“ celistitem0002”> • 对于同构正惩罚，我们证明了最优解可以可以通过两个步骤获得：近端算子和归一化步骤。对于一般罚款，我们通过解决对偶问题提供了一种通用算法。 • 我们提供了一些算法，可为几种非凸罚分找到分析解决方案，包括MCP，ℓ 0 范数，以及排序后的ℓ 1 惩罚。 • 这些分析解决方案使算法比现有1bit-CS快得多，算法比现有1bit-CS快得多-CS用于非凸罚分的算法，甚至可以与凸ℓ 1 最小化问题的算法相提并论。 • 这些分析解决方案使人们能够分析诸如作为非凸罚分的采样复杂度es，这超出了本文的重点。 < ce：abstract xmlns：ce =“ http://www.elsevier.com/xml/common/dtd” xmlns =“ http://www.elsevier.com/xml/ja/dtd” id =“ abs0001” class = “作者” view =“ all”> 摘要 0 范数和排序ℓ 1 惩罚。具体来说，我们的算法比现有的MCP算法快200倍以上。它的效率可与ℓ 1 及时惩罚的算法相比，而其性能远优于than 1 。在这些罚则中，排序ce 1 在不同设置下对噪声最强。

著录项

  • 来源
    《Signal processing》 |2018年第3期|341-351|共11页
  • 作者

    Xiaolin Huang; Ming Yan;

  • 作者单位

    Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, and MOE Key Laboratory of System Control and Information Processing;

    Department of Computational Mathematics, Science and Engineering and Department of Mathematics, Michigan State University;

  • 收录信息
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    One-bit compressed sensing; Non-convex penalty; Analytical solutions;

    机译：一比特压缩传感;非凸罚分;解析解;

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号