A differential equations approach to l1-minimization with applications to array imaging
A differential equations approach to l1-minimization with applications to array imaging
复制标题
L1 最小化的微分方程方法及其在阵列成像中的应用
DOI：
10.1088/0266-5611/28/10/105001
复制
发表时间：
2012
期刊：
影响因子：
2.1
通讯作者：
L. Ryzhik
中科院分区：
文献类型：
--
作者：
M. Moscoso;A. Novikov;G. Papanicolaou;L. Ryzhik
我们提出了一种常微分方程法来分析构造满秩欠定线性系统的L1极小解的算法。它涉及到一个松弛极小化问题，其最小值与松弛参数无关。使用常微分方程组的一个优点是可以使用能量方法来证明收敛。单调非线性半群的Crandall-Liggett理论提供了与离散算法的联系。通过算例说明了离散优化算法在稀疏阵列成像问题中的有效性。
We present an ordinary differential equation approach to the analysis of algorithms for constructing l1 minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall–Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse array imaging problems.