We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this approach to handle errors in the sensing vectors by adopting the total least squares (TLS) framework familiar from linear inverse problems with operator errors. We show how gradient descent and the peculiar geometry of the phase retrieval problem can be used to obtain a simple and efficient TLS solution. Additionally, we derive the gradients of the TLS and LS solutions with respect to the sensing vectors and measurements which enables us to calculate the solution errors. By analyzing these error expressions we determine when each method should perform well. We run simulations to demonstrate the benefits of our method and verify the analysis. We further demonstrate the effectiveness of our approach by performing phase retrieval experiments on real optical hardware which naturally contains sensing vector and measurement errors.

翻译：我们用遥感矢量的错误来解决阶段检索问题。一些最近的阶段检索方法基于最小平方(LS)的配方,这些配方假定了二次测量中的错误。我们推广了这种方法,通过采用从操作员错误的线性反向问题中熟悉的总最小方(TLS)框架来处理遥感矢量的错误。我们展示了如何利用梯度下降和阶段检索问题的特殊几何来获得简单有效的 TLS 解决方案。此外,我们从遥感矢量和测量中得出TLS和LS解决方案的梯度,这些梯度使我们能够计算出解决方案的错误。我们通过分析这些错误的表达方式确定每种方法应何时运行良好。我们进行模拟,以展示我们方法的效益并核实分析结果。我们进一步展示了我们的方法的有效性,对自然含有感测矢量和测量错误的真正光硬件进行阶段检索实验。