在相位恢复过程中,用图像的稀疏性作为先验知识可以提高图像的重构质量。结合图像在小波域的组稀疏性与图像自身的梯度稀疏性,针对编码衍射图样模型,提出一种融合正交小波db10和sym4组稀疏性与全变差正则化的相位恢复算法。针对当前相位恢复算法重构时间较长的问题,采用复合分裂算法将非凸优化问题分解成几个易于求解的子问题(包括两个组硬阈值算子和全变差最小化)进行求解,减少了图像重构时间。实验结果表明:在高斯噪声下,与BM3D-PRGAMP算法相比,所提算法重构图像的峰值信噪比提高了约0.8 dB,重构时间缩短了90%;在泊松模型中,所提算法也具有较大优势,充分说明了所提算法对噪声具有稳健性。

In process of phase retrieval, the image reconstruction quality can be improved when we use the image sparsity as the prior knowledge. By combining the group sparsity of image in wavelet domain with the gradient sparsity of the image itself, we propose a phase retrieval algorithm fusing orthogonal wavelet db10, sym4 group sparsity and total variation regularization for the coded diffraction pattern model. Aiming at the problem that reconfiguration time of the current phase retrieval algorithm is long, we use composite splitting algorithm to decompose nonconvex optimization problem into several sub-problems (including two group hard threshold operators and total variation minimization) that can be solved easily, which reduces the image reconstruction time. Experimental results show that the peak signal-to-noise ratio of the reconstructed image obtained by the proposed algorithm is improved by about 0.8 dB compared with that of BM3D-PRGAMP algorithm under Gaussian noise, and the reconstruction time is reduced by 90%. In Poisson model, the proposed algorithm also has a great advantage, which fully demonstrates that the algorithm is robust to noise.