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精确和稳定的具有稀疏的增量通过微分ℓ1最小化恢复信号序列Exact and Stable Recovery of Sequences of Signals with Sparse Increments via Differential ℓ1-Minimization |
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| 课程网址: | http://videolectures.net/machine_ba_sparse/ |
| 主讲教师: | Demba Ba |
| 开课单位: | 麻省理工学院 |
| 开课时间: | 2013-01-14 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider the problem of recovering a sequence of vectors, (xk)k=0K, for which the increments xk−xk−1 are Sk-sparse (with Sk typically smaller than S1), based on linear measurements (yk=Akxk+ek)k=1K, where Ak and ek denote the measurement matrix and noise, respectively. Assuming each Ak obeys the restricted isometry property (RIP) of a certain order - depending only on Sk - we show that in the absence of noise a convex program, which minimizes the weighted sum of the ℓ1-norm of successive differences subject to the linear measurement constraints, recovers the sequence (xk)k=1K emph{exactly}. This is an interesting result because this convex program is equivalent to a standard compressive sensing problem with a highly-structured aggregate measurement matrix which does not satisfy the RIP requirements in the standard sense, and yet we can achieve exact recovery. In the presence of bounded noise, we propose a quadratically-constrained convex program for recovery and derive bounds on the reconstruction error of the sequence. We supplement our theoretical analysis with simulations and an application to real video data. These further support the validity of the proposed approach for acquisition and recovery of signals with time-varying sparsity. |
| 关 键 词: | 恢复序列的问题; 矩阵; 精确恢复; 有界噪声 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-01：吴雨秋(课程编辑志愿者) |
| 阅读次数: | 24 |