Nonconvex Demixing from Bilinear Measurements

We consider the problem of demixing a sequence of source signals from the sum of bilinear measurements. It is a generalized mathematical model of blind demixing with deconvolution, which has wide applications in communication, image processing and dictionary learning, etc. However, state-of-art algorithms for blind demixing either fail to scale to large problem sizes or require proper regularization with tedious algorithmic parameters for optimality guarantees. To address the limitations of exiting methods, we propose a provable nonconvex demixing procedure via Wirtinger flow, much like vanilla gradient descent, to harness the benefits of regularization free, fast convergence rate, and optimality guarantees. This is achieved by exploiting the benign geometry of blind demixing, thereby revealing that Wirtinger flow enforces the iterates in the region of strong convexity and qualified level of smoothness.