Matrix Recovery using Deep Generative Priors with Low-Rank Deviations

In matrix recovery, an unknown matrix can be reconstructed by a small number of limited and noisy measurements. Deep learning-based methods, such as deep generative models, provide stronger priors that can serve to mitigate the pressure of sampling during image recovery. But such methods require that the recovered data be limited to the scope of the generator, otherwise it will lead to large recovery error. To circumvent this problem, in this paper, a framework for matrix recovery from limited measurements is proposed, which employs low rank approximation to characterize the deviation of generator, referred to as Low-Rank-Gen. Theoretically, we propose Matrix Set-Restricted Eigenvalue Condition (M-S-REC), and further prove the existence of decoders and upper bound of reconstruction error using certain number of measurements corresponding to such decoder. Empirically, we observe consistent improvements in reconstruction accuracy, PSNR index, and noise tolerance over competing approaches.