# Low-Rank Phase Retrieval with Structured Tensor Models. (arXiv:2202.08260v1 [eess.IV])

We study the low-rank phase retrieval problem, where the objective is to
recover a sequence of signals (typically images) given the magnitude of linear
measurements of those signals. Existing solutions involve recovering a matrix
constructed by vectorizing and stacking each image. These algorithms model this
matrix to be low-rank and leverage the low-rank property to decrease the sample
complexity required for accurate recovery. However, when the number of
available measurements is more limited, these low-rank matrix models can often
fail. We propose an algorithm called Tucker-Structured Phase Retrieval (TSPR)
that models the sequence of images as a tensor rather than a matrix that we
factorize using the Tucker decomposition. This factorization reduces the number
of parameters that need to be estimated, allowing for a more accurate
reconstruction in the under-sampled regime. Interestingly, we observe that this
structure also has improved performance in the over-determined setting when the
Tucker ranks are chosen appropriately. We demonstrate the effectiveness of our
approach on real video datasets under several different measurement models.