Distributed signal recovery based on in-network subspace projections

We study distributed processing of subspace-constrained signals in multi-agent networks with sparse connectivity. We introduce the first optimization framework based on distributed subspace projections, aimed at minimizing a network cost function depending on the specific processing task, while imposing subspace constraints on the final solution. The proposed method hinges on (sub)gradient techniques while leveraging distributed projections as a mechanism to enforce subspace constraints in a cooperative and distributed fashion. Asymptotic convergence to optimal solutions of the problem is established under different assumptions (e.g., nondifferentiability, nonconvexity, etc.) on the objective function. Finally, numerical tests assess the performance of the proposed distributed strategy.