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Iterative thresholding methods have been extensively studied as faster alternatives to convex optimization methods for solving large-sized problems in compressed sensing MRI. A novel iterative thresholding method, called LCAMP (Location Constrained Approximate Message Passing), is presented for reducing computational complexity and improving reconstruction accuracy when a non-zero location (or sparse support) constraint can be obtained from view shared images in dynamic contrast-enhanced MRI (DCE-MRI). LCAMP modifies the existing approximate message passing algorithm by replacing the thresholding stage with a location constraint, which avoids adjusting regularization parameters or thresholding levels. This work is applied to breast DCE-MRI to demonstrate the excellent reconstruction accuracy and low computation time with highly undersampled data.