Blind Demixing via Wirtinger Flow with Random Initialization
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:362-370, 2019.
This paper concerns the problem of demixing a series of source signals from the sum of bilinear measurements. This problem spans diverse areas such as communication, imaging processing, machine learning, etc. However, semidefinite programming for blind demixing is prohibitive to large-scale problems due to high computational complexity and storage cost. Although several efficient algorithms have been developed recently that enjoy the benefits of fast convergence rates and even regularization free, they still call for spectral initialization. To find simple initialization approach that works equally well as spectral initialization, we propose to solve blind demixing problem via Wirtinger flow with random initialization, which yields a natural implementation. To reveal the efficiency of this algorithm, we provide the global convergence guarantee concerning randomly initialized Wirtinger flow for blind demixing. Specifically, it shows that with sufficient samples, the iterates of randomly initialized Wirtinger flow can enter a local region that enjoys strong convexity and strong smoothness within a few iterations at the first stage. At the second stage, iterates of randomly initialized Wirtinger flow further converge linearly to the ground truth.