图 书 馆
稀疏恢复的快速方法：L1的替代方法Fast methods for sparse recovery: alternatives to L1 |
|
| 课程网址: | http://videolectures.net/smls09_davies_fmfsr/ |
| 主讲教师: | Mike Davies |
| 开课单位: | 爱丁堡大学 |
| 开课时间: | 2009-05-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. Recent theoretical advances in our understanding of this problem have further increased interest in their application to various domains. In many areas, such as for example medical imaging or geophysical data acquisition, it is necessary to find sparse solutions to very large underdetermined inverse problems. Fast methods therefore have to be developed. In this talk, we will present two classes of fast algorithm that are competitive with the more classical L1 minimization (Basis Pursuit). The first techniques is based upon a greedy selection approach. However in each iteration, several new elements are selected. The selected coefficients are then updated using a conjugate update direction. This is an extension of the previously suggested Gradient Pursuit framework to allow an even greedier selection strategy. It also has the unique property of allowing a smooth trade-off between recovery performance and computational complexity. The second technique that we discuss is an extremely simple strategy called Iterative Hard thresholding (IHT). Despite its simplicity it can be shown that: it gives near-optimal performance guarantees; it is robust to observation noise; it has low bounded computational complexity per iteration and only requires a fixed number of iterations depending on the signal to noise ratio of the signal. Unfortunately a niaive application of IHT yields empirical performance substantially below that of other state of the art recovery algorithms. We therefore discuss have the algorithm can be modified to obtain performance that is comparable with state of the art while retaining its strong theoretical properties. |
| 关 键 词: | 信号源; 地球物理数据; 欠定反问题 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-05-22：杨雨(课程编辑志愿者) |
| 阅读次数: | 86 |