论文标题
可分离的多块多块凸优化和压缩仿射相的惯性近端ADMM
Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations and Compressive Affine Phase Retrieval
论文作者
论文摘要
可分离的多块凸优化问题出现在许多数学和工程领域中。在本文的第一部分中，我们提出了一个惯性近端ADMM来解决线性约束的可分离多块凸凸优化问题，并且我们表明，在正则化矩阵上，提出的拟议惯性近端ADMM具有在温和的假设下具有全球收敛性。仿射期检索是在全息图，数据分离和无相度抽样的过程中引起的，并且也被认为是相位检索的非均匀版本，近年来受到了相当大的关注。在本文的第二部分中，受到压缩感感应和相位检索的相位凸起的凸起的启发，我们通过提升方法引入了一种压缩仿射阶段检索，以将仿射相结合的方法与多块构造的优化连接起来，然后基于提议的惯性稳定性，以实现暂时的稳定性，以恢复多种序列化，以恢复多种序列，以恢复序列化，以恢复序列化，以恢复序列化的稳定性，并恢复综合，以恢复稳定性，并恢复稳定性。来自其（嘈杂的）仿射二次测量的真实信号。我们的数值模拟表明，所提出的算法对于稀疏真实信号的仿射相检索具有令人满意的性能。
Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem, and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices. Affine phase retrieval arises in holography, data separation and phaseless sampling, and it is also considered as a nonhomogeneous version of phase retrieval that has received considerable attention in recent years. Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval, in the second part of this paper, we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization, and then based on the proposed inertial proximal ADMM for multi-block convex optimization, we propose an algorithm to recover sparse real signals from their (noisy) affine quadratic measurements. Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.
