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The augmented Lagrangian frame work with the different sub problems. The original problem in (3) is broken into a series of multiple simpler problems by using the augmented Lagrangian framework. Specifically, the algorithm iterates between the steps of regularized SENSE (that is solved by the method of conjugate gradient (CG)), singular value shrinkage, shrinkage and update rules for Lagrange multipliers. These steps are all solved by simple operations.
