全最小二乘相位恢复
Total Least Squares Phase Retrieval
摘要：
我们解决了相位恢复问题的传感矢量中的错误。许多最近的相位恢复方法是基于最小二乘（LS）配方，假设在二次测量的错误。我们扩展这种方法来处理的传感向量中的错误，采用总最小二乘（TLS）的框架，用于线性逆问题与操作员的错误。我们展示了如何梯度下降和相位恢复问题的特定几何形状可以用来获得一个简单而有效的TLS解决方案。此外，我们推导出TLS和LS解决方案相对于传感矢量和测量的梯度，这使我们能够计算解决方案的误差。通过分析这些错误表达式，我们确定了每种方法应该优于另一种方法的条件。我们运行模拟，以证明我们的方法可以导致更准确的解决方案。我们进一步证明了我们的方法的有效性，通过进行相位恢复实验，真实的光学硬件，自然包含传感矢量和测量误差。
英文摘要：
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 that is used in linear inverse problems with operator errors. We show how gradient descent and the specific 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 conditions under which each method should outperform the other. We run simulations to demonstrate that our method can lead to more accurate solutions. We further demonstrate the effectiveness of our approach by performing phase retrieval experiments on real optical hardware which naturally contains both sensing vector and measurement errors.
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