摘要
A newalgorithm, called Magnitude Cut, to recover a signal from its phase in the transform domain, is proposed.First, the recovery problem is converted to an equivalent convex optimization problem, and then it is solved by the block coordinate descent（ BCD） algorithm and the interior point algorithm. Finally, the one-dimensional and twodimensional signal reconstructions are implemented and the reconstruction results under the Fourier transform with a Gaussian random mask（ FTGM）, the Cauchy wavelets transform（ CWT）, the Fourier transform with a binary random mask（ FTBM） and the Gaussian random transform（ GRT） are also comparatively analyzed. The analysis results reveal that the M agnitude Cut method can reconstruct the original signal with the phase information of different transforms; and it needs less phase information to recover the signal from the phase of the FTGM or GRT than that of FTBM or CWT under the same reconstruction error.
提出了一种新的算法——Magnitude Cut算法,用于从信号的变换域的相位来恢复信号.首先将重建问题等价转换为一个凸优化问题,然后通过块坐标下降算法(BCD)和内点法解决原始信号重建问题.最后,实现了一维和二维信号的重建,并对先通过高斯随机掩膜再进行傅里叶变换(简称FTGM),柯西小波变换(CWT)相位,先通过二值随机掩膜再进行傅里叶变换(简称FTBM),高斯随机变换(GRT)相位的信号重建结果做了比较分析.分析结果表明,Magnitude Cut算法可以完成已知信号不同变换域相位的信号重建,并且在相同的重建误差下,从FTGM和GRT相位信息重建信号比从FTBM和CWT需要的相位数目更少.
基金
The National Natural Science Foundation of China(No.61201344
61271312
11301074)
the Specialized Research Fund for the Doctoral Program of Higher Education(No.20110092110023
20120092120036)
the Program for Special Talents in Six Fields of Jiangsu Province(No.DZXX-031)
the Natural Science Foundation of Jiangsu Province(No.BK2012329
BK2012743)
the United Creative Foundation of Jiangsu Province(No.BY2014127-11)
the"333"Project(No.BRA2015288)
