Fast BCS-FOCUSS and DBCS-FOCUSS with augmented Lagrangian and minimum residual methods

Abstract Block compressive sensing FOCal Underdetermined System Solver (BCS-FOCUSS) and distributed BCS-FOCUSS (DBCS-FOCUSS) are iterative algorithms for individual and joint recovery of correlated images. The performance of both these algorithms was noticed to be best within BCS framework. However, both these algorithms suffer from high computational complexity and recovery time. This is caused by the need for an explicit computation of matrix inverse in each iteration and a slow convergence from a poor starting point. In this paper, we propose a methodology to obtain fast and good initial solution using the augmented Lagrangian method to improve the convergence rate of both algorithms. We also propose to incorporate the minimum residual method to avoid matrix inversion to reduce the computational cost. Simulation studies with the proposed modified BCS-FOCUSS and DBCS-FOCUSS demonstrate a significant reduction in the computational cost and recovery time while improving reconstruction quality for both individual and joint reconstruction algorithms.