A method for estimating a coil sensitivity map for a magnetic resonance (MR) image includes providing a matrix A of sliding blocks of a 3D image of coil calibration data, calculating a left singular matrix V∥ from a singular value decomposition of A corresponding to τ leading singular values, calculating P=V∥V∥H, calculating a matrix that is an inverse Fourier transform of a zero-padded matrix P, and solving MHcr=(Sr)Hcr for cr, where cr is a vector of coil sensitivity maps for all coils at spatial location r, and M = ( ( 1 1 … 1 0 0 … 0 … … … 0 0 … 0 ) ⁢ ( 0 0 … 0 1 1 … 1 … … … 0 0 … 0 ) ⁢ ⁢ … ⁢ ⁢ ( 0 0 … 0 0 0 … 0 … … … 1 1 … 1 ) ) .