Distributed and Consensus Optimization for Non-smooth Image Reconstruction

We present a primal-dual algorithm with consensus constraints that can effectively handle large-scale and complex data in a variety of non-smooth image reconstruction problems. In particular, we focus on the case that the data fidelity term can be decomposed into multiple relatively simple functions and deployed to parallel computing units to cooperatively solve for a consensual solution of the original problem. In this case, the subproblems usually have closed form solution or can be solved efficiently at local computing units, and hence the per-iteration computation complexity is very low. A comprehensive convergence analysis of the algorithm, including convergence rate, is established.