Dec-AltProjGDmin: Fully-Decentralized Alternating Projected Gradient Descent for Low Rank Column-wise Compressive Sensing.

This work develops a fully-decentralized alternating projected gradient descent algorithm, called Dec-AltProjGDmin, for solving the following low-rank (LR) matrix recovery problem: recover an LR matrix from independent columnwise linear projections (LR column-wise Compressive Sensing). We prove its correctness under simple assumptions and argue that Dec-AltProjGDmin is both faster and more communication-efficient than various other potential solution approaches, in addition to also having one of the best sample complexity guarantees. To our best knowledge, this work is the first attempt to develop a provably correct fully-decentralized algorithm for any problem involving the use of an alternating projected GD algorithm when the constraint set (the set to be projected onto) is non-convex.