This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning.
翻译:本文论述在多种防毒系统应用的各种结构性限制下,在各种结构性限制下微弱的信号重建; 侧面限制可能来自先前关于测量系统和稀薄信号结构的信息,可能涉及感测矩阵的结构、非零支持值的结构、稀散代表器的时间结构和非线性测量结构; 首先,我们用L1-最小化的方式,展示结构性限制形式的先验信息如何影响恢复保障(Null空间特性); 此外,对于恒定模量信号、行、区块和排级差的信号以及非循环信号,我们说明如何利用先前的结构信息设计高效的算法,同时改进恢复性能和降低计算复杂性; 最后,我们讨论对稀散信号进行线性和非线性测量的测量系统设计; 此外,我们讨论以一致性最小化为基础的线性混合矩阵设计; 然后,我们把重点扩大到非线性测量系统,我们设计平行的优化算法,以便有效地计算稀薄阶段检索问题中的站点,而不进行字典学习。