Abstract: 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.