图 书 馆
压缩传感中的相变现象Phase transitions phenomenon in Compressed Sensing |
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| 课程网址: | http://videolectures.net/smls09_tanner_ptpics/ |
| 主讲教师: | Jared Tanner |
| 开课单位: | 牛津大学 |
| 开课时间: | 2009-05-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Compressed Sensing reconstruction algorithms typically exhibit a zeroth-order phase transition phenomenon for large problem sizes, where there is a domain of problem sizes for which successful recovery occurs with overwhelming probability, and there is a domain of problem sizes for which recovery failure occurs with overwhelming probability. The mathematics underlying this phenomenon will be outlined for $\ell1$ regularization and non-negative feasibility point regions. Both instances employ a large deviation analysis of the associated geometric probability event. These results give precise if and only if conditions on the number of samples needed in Compressed Sensing applications. Lower bounds on the phase transitions implied by the Restricted Isometry Property for Gaussian random matrices will also be presented for the following algorithms: $\ell^q$-regularization for $q\in (0,1]$, CoSaMP, Subspace Pursuit, and Iterated Hard Thresholding. |
| 关 键 词: | 计算机科学; 机器学习; 压缩传感 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-05-30：张荧(课程编辑志愿者) |
| 阅读次数: | 92 |