ADMM based Consensus and Sectioning Norm-1 Regularized Algorithm for Imaging with a CRA

A norm-1 regularized, distributed technique based on the Alternating Direction Method of Multipliers (ADMM) is presented in this paper. This method divides the sensing matrix of the problem in both rows and columns, leading to the so-called consensus and sectioning-based ADMM, which incorporates the convergence properties of the consensus-based ADMM with the communication efficiency of the sectioning-based ADMM. A Compressive Reflector Antenna (CRA) has been recently proposed as a hardware to increase the sensing capacity of the imaging systems. The combination of the consensus and sectioning-based ADMM with a CRA allows a quasi real-time imaging with high communication efficiency.