Separable optimization for joint blind deconvolution and demixing

Blind deconvolution and demixing is the problem of reconstructing convolved signals and kernels from the sum of their convolutions. This problem arises in many applications, such as blind MIMO. In this work, we present a separable approach to blind deconvolution and demixing via convex optimization. Unlike previous works, our formulation allows separation into smaller optimization problems, allowing significantly improved complexity. We demonstrate the near optimal performance of our method, in accordance with the theoretical guarantees of the original, non-separable problem, under several normalization constraints.