Methods, systems, and apparatuses for non-convex prior image constrained compressed sensing are disclosed. In one embodiment, a method is provided for iterative image reconstruction for medical imaging applications which employ a prior image to constrain the reconstruction process allowing the use of fewer high SNR samples or complete but lower SNR samples. The objective function made use of non-convex compressed sensing methods during the iterative reconstruction process. Applications include, but are not limited to radiation dose reduction and fast image acquisition.