An Algorithm Solving Compressive Sensing Problem Based on Maximal Monotone Operators
An Algorithm Solving Compressive Sensing Problem Based on Maximal Monotone Operators
复制标题
一种基于最大单调算子的压缩感知问题求解算法
DOI：
10.1137/19m1260670
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发表时间：
2021
影响因子：
3.1
通讯作者：
Serna, Susana
中科院分区：
文献类型：
--
作者：
Tendero, Yohann;Ciril, Igor;Darbon, Jérôme;Serna, Susana
解决正则化线性问题的需要可以由数据分析和信号或图像处理的各种压缩感知和稀疏相关技术激发。这些问题导致了高维的非光滑凸优化。理论工作预测了压缩感知问题精确恢复的急剧相变。我们的数值实验表明，最先进的算法不足以有效地观察这种相变。本文提出了一个简单的形式，使我们能够在对机器精度的约束下产生一个计算最小化器的算法。此外，还展示了与文献中可用的标准算法的数值比较。对比表明，我们的算法在精度和效率方面都优于其他最先进的方法。该算法可以高精度地观测到上述相变。
The need to solveregularized linear problems can be motivated by various compressive sensing and sparsity related techniques for data analysis and signal or image processing. These problems lead to nonsmooth convex optimization in high dimensions. Theoretical works predict a sharp phase transition for the exact recovery of compressive sensing problems. Our numerical experiments show that state-of-the-art algorithms are not effective enough to observe this phase transition accurately. This paper proposes a simple formalism that enables us to produce an algorithm that computes anminimizer under the constraintsup to the machine precision. In addition, a numerical comparison with standard algorithms available in the literature is exhibited. The comparison shows that our algorithm compares advantageously with other state-of-the-art methods, both in terms of accuracy and efficiency. With our algorithm, the aforementioned phase transition is observed at high precision.
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影响因子：
2.1
作者：
Beck, Amir;Teboulle, Marc
通讯作者：
Teboulle, Marc
DOI：
10.1073/pnas.0437847100
发表时间：
2003-03-04
影响因子：
11.1
作者：
Donoho, DL;Elad, M
通讯作者：
Elad, M
一种简单的二次规划新算法及其在统计中的应用
DOI：
--
发表时间：
2013
期刊：
Communications in statistics. Simulation and computation
影响因子：
--
作者：
Mary C. Meyer
通讯作者：
Mary C. Meyer
影响因子：
1.6
作者：
Osher, S;Burger, M;Yin, WT
通讯作者：
Yin, WT