基于相位割的相位检索

Phase Retrieval Based on PhaseCut

相位提升将具有非线性约束的相位检索问题转化为半正定规划问题,是一种研究相位检索的新方法.通过精确地分离振幅和相位变量,结合相位提升方法,相位检索问题成为一个类似于最大割半正定规划问题——相位割.随着问题尺寸的增大,相位割问题的计算量快速增大,为此,文中提出利用适合解决最大割问题的PURE-RBR-M算法来求解相位割.模拟实验结果表明:PURE-RBR-M算法可以成功实现相位检索,且对有噪声的测量是鲁棒的;与内点算法和贪婪算法相比,PURE-RBR-M算法运算速度快,可快速地实现信号的重构.

PhaseLift is a new phase retrieval method that converts phase retrieval problems with nonlinear constraints into semidefinite programming problems. Phase retrieval problems are translated into Maxcut-like semidefinite programming problems （namely PhaseCut） by accurately separating amplitude and phase variables combined with the method of PhaseLift. As the computational complexity of PhaseCut increases quickly with the problem size, a PURE-RBR-M algorithm suitable for MaxCut problems is employed to solve PhaseCut. Simulated results show that PURE-RBR-M algorithm achieves phase retrieval successfully and possesses strong robustness to noise measurement ; and that it is superior to the interior point algorithm and the greedy algorithm because it runs faster and leads to a quicker signal reconstruction.