1. A magnetic resonance imaging (MRI) system comprising: an MRI gantry including static and gradient magnetic field generators, at least one radio frequency (RF) coil and RF transmitter and receiver circuits configured to transmit nuclear magnetic resonance (NMR) RF excitation pulses into an imaging volume and to receive NMR RF response signals from patient tissue located in the imaging volume; and at least one control circuit connected to said gradient magnetic field generators and said RF transmitter and receiver circuits, said control circuits being configured to: (a) perform a sparse acquisition of k-space data corresponding to NMR signals received by each RF coil; (b) estimate, using the acquired sparse k-space data, a sensitivity map for each RF coil; (c) reconstruct an MR image using compressed sensing based upon the at least one sensitivity map by minimizing a predetermined function which is based upon the MR image and coefficients of the at least one sensitivity map; (d) update the at least one sensitivity map by minimizing the predetermined function; (e) iteratively perform the reconstruct and the update processes (c) and (d) until at least one of the following conditions occur: (1) an operator selects to end iterating, or (2) the predetermined function converges; and (f) output the reconstructed MR image when at least one of the conditions occur.