A method for reconstructing parallel magnetic resonance images includes providing a set of acquired k-space MR image data y, and finding a target MR image x that minimizes ½∥Fv−y∥22+λ∥z∥1 where v=Sx and z=Wx where S is a diagonal matrix containing sensitivity maps of coil elements in an MR receiver array, F is an FFT matrix, W is a redundant Haar wavelet matrix, and λ≧0 is a regularization parameter, by updatingxk+1=(μ1I+μ3SHS)-1[μ1WH(zk-bzk)+μ3SH(vk-bvk)],zk+1=soft(Wxk+1+bzk,1μ1)where soft(x,T)={x+Tifx≤-T,0ifx≤T,x-Tifx≥T,andvk+1=(FHF+μ3I)-1[FHy+μ3(Sxk+1+bvk)], where k is an iteration counter, μ1 and μ3 are parameters of an augmented Lagrangian function, and bz and bv are dual variables of the augmented Lagrangian.
