This paper discusses algorithms for phase retrieval where the measurements follow independent Poisson distributions, using maximum likelihood (ML) estimation. To optimize the log-likelihood for the Poisson phase retrieval model, we developed and compared several algorithms including Wirtinger flow (WF), Gerchberg Saxton (GS), majorize minimize (MM) and alternating direction method of multipliers (ADMM). Simulation results using random Gaussian sensing matrix, discrete Fourier transform (DFT) matrix and an empirical transmission matrix under Poisson measurement noise demonstrated that algorithms based on the Poisson model consistently produced higher quality reconstructions than algorithms (WF, GS) derived from Gaussian noise models when applied to such data. Moreover, the reconstruction quality can be further improved by adding regularizers that exploit assumed properties of the latent signal/image, such as sparsity of finite differences (anisotropic total variation) or of the coefficients of a discrete wavelet transform.

翻译：本文讨论采用最大可能性( ML) 估计测算法进行独立的 Poisson 分布的阶段检索的算法。 为了优化 Poisson 阶段检索模型的日志相似性,我们开发并比较了几种算法,包括Wirtinger 流(WF)、Gerchberg Saxton(GS)、主要最小化(MM)和乘数交替方向法(ADMM)。 使用随机高斯感测矩阵、离散的 Fourier变异(DFT) 矩阵和Poisson 测量噪音下的经验传输矩阵的模拟结果显示,基于 Poisson 模型的算法在应用Gaussian 噪音模型(WF、GS) 的算法(WF、GS), 其质量的重建质量一直高于这些数据时产生的算法(WF、GS) 。 此外,可以通过增加利用潜在信号/影像的假定特性的正规化者来进一步改进重建质量, 如定点差异(异总变) 或离波变系数的宽度。