压缩感知中基于FADMM的l_1-l_1范数信号重构

L1-L1 NORM SIGNAL RECONSTRUCTION BASED ON FADMM FOR COMPRESSED SENSING

为解决极小化l_1-l_1范数难以求解的问题,采用一种带有"重启动"规则的快速交替方向乘子法FADMM(Fast Alternating Direction Method of Multipliers)对该模型求解。通过引入辅助变量,将l_1-l_1模型分裂为两个易于求解的子问题,采用线性化技巧使每个子问题都存在解析解,交替更新原始及对偶变量,并在迭代过程中执行变量的二次更新,同时引入重启动策略以保证算法的全局收敛性。FADMM在求解过程中无需将l_1-l_1模型转化为等价的基追踪BP(Basis Pursuit)问题且不要求感知矩阵行正交。仿真结果验证了该方法的可行性与有效性。

A fast alternating direction method of multipliers（ FADMM） with restart ruleis proposed to solve the problem of minimizing the l_1-l_1 norm. By introducing an auxiliary variable,the l_1-l_1 model was separated into two sub-problems which were easy to solve. And the linearization operation was used to make every sub-problem had an analytical solution. The algorithm updated the primal and dual variables alternately,and then updated variables for the second time. The restart strategy was also introduced to ensure the global convergence. In the calculation process,there was no need to translate the l_1-l_1 model into an equivalent basis pursuit（ BP） problem,and did not require the row orthogonality of sensing matrix. Simulation results show the feasibility and effectiveness of the proposed method.