Phase Retrieval by Tensor Total Least Squares

Phase retrieval seeks to reconstruct a series of image sequences from measurements that only capture their magnitudes. Current approaches either flatten and stack the image sequences, disregarding their multidimensional structural information, or fail to account for errors within the sensing vectors/tensors. To address these two issues simultaneously, we propose a unified framework for the phase retrieval problem, namely tensor total least squares (TTLS). Specifically, we set up a tensor representation for image sequences and the corresponding measurement model, and for the first time employ the advanced tensor ring network to effectively explore the inherent multidimensional structure for more accurate estimation. Moreover, in addition to the additive noise, the multiplicative errors within the sensing tensor can be also well-corrected, leading to a more robust estimation. Experimental results on both simulated data and real videos demonstrate the superiority of the proposed method.