Accelerated Schemes for the <inline-formula><tex-math notation="LaTeX">$L_1/L_2$</tex-math></inline-formula> Minimization
Accelerated Schemes for the <inline-formula><tex-math notation="LaTeX">$L_1/L_2$</tex-math></inline-formula> Minimization
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DOI：
10.1109/tsp.2020.2985298
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发表时间：
2020-01-01
影响因子：
5.4
通讯作者：
Lou, Yifei
中科院分区：
文献类型：
--
作者：
Wang, Chao;Yan, Ming;Lou, Yifei
本文考虑了稀疏恢复的极小化问题，并研究了它与模型的关系。基于这种关系，我们提出了三个数值算法来最小化这个比例模型，其中两个工作作为自适应计划，大大减少了计算时间。集中在两个自适应计划，我们讨论了它们与现有方法的连接，并分析了它们的收敛性。实验结果表明，所提出的算法是国家的最先进的方法在稀疏恢复和工作时，地面实况信号具有高的动态范围特别好。最后，我们揭示了一些经验证据下的稀疏性，一致性和动态范围，这需要在未来的理论论证的各种组合的确切恢复。
In this paper, we consider the minimization for sparse recovery and study its relationship with the model. Based on this relationship, we propose three numerical algorithms to minimize this ratio model, two of which work as adaptive schemes and greatly reduce the computation time. Focusing on the two adaptive schemes, we discuss their connection to existing approaches and analyze their convergence. The experimental results demonstrate that the proposed algorithms are comparable to state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. Lastly, we reveal some empirical evidence on the exact recovery under various combinations of sparsity, coherence, and dynamic ranges, which calls for theoretical justification in the future.