A method for producing a plurality of images of a subject with a magnetic resonance imaging system, the steps of the method comprising: a) directing an MRI system to perform a pulse sequence comprising: applying a radio frequency excitation field to a portion of a subject that includes a plurality of slice locations, the plurality of slice locations including a current slice location and at least one adjacent slice location, the RF excitation field exciting spins in the plurality of slice locations; establishing at least one alternating readout magnetic field gradient along a frequency-encoding direction following the application of the RF excitation field in order to form echo signals; sequentially producing a plurality of slice-encoding magnetic field gradient blips along a slice-encoding direction while the at least one alternating readout magnetic field gradient is established, each sequential slice-encoding magnetic field gradient blip having a randomly assigned magnitude such that a random phase shift related to the randomly assigned magnitude is imparted to the formed echo signals; b) acquiring data with an array of RF receiver coils by sampling the formed echo signals; c) estimating a sensitivity map for each RF receiver coil in the array of RF receiver coils; and d) reconstructing at least one image for each of the plurality of slice locations from the data acquired in step b) using a compressed sensing framework that accounts for the random phase shifts imparted to the formed echo signals by incorporating the random phase shifts and each sensitivity map into a forward model. a) directing an MRI system to perform a pulse sequence comprising: applying a radio frequency excitation field to a portion of a subject that includes a plurality of slice locations, the plurality of slice locations including a current slice location and at least one adjacent slice location, the RF excitation field exciting spins in the plurality of slice locations; establishing at least one alternating readout magnetic field gradient along a frequency-encoding direction following the application of the RF excitation field in order to form echo signals; sequentially producing a plurality of slice-encoding magnetic field gradient blips along a slice-encoding direction while the at least one alternating readout magnetic field gradient is established, each sequential slice-encoding magnetic field gradient blip having a randomly assigned magnitude such that a random phase shift related to the randomly assigned magnitude is imparted to the formed echo signals; applying a radio frequency excitation field to a portion of a subject that includes a plurality of slice locations, the plurality of slice locations including a current slice location and at least one adjacent slice location, the RF excitation field exciting spins in the plurality of slice locations; establishing at least one alternating readout magnetic field gradient along a frequency-encoding direction following the application of the RF excitation field in order to form echo signals; sequentially producing a plurality of slice-encoding magnetic field gradient blips along a slice-encoding direction while the at least one alternating readout magnetic field gradient is established, each sequential slice-encoding magnetic field gradient blip having a randomly assigned magnitude such that a random phase shift related to the randomly assigned magnitude is imparted to the formed echo signals; b) acquiring data with an array of RF receiver coils by sampling the formed echo signals; c) estimating a sensitivity map for each RF receiver coil in the array of RF receiver coils; and d) reconstructing at least one image for each of the plurality of slice locations from the data acquired in step b) using a compressed sensing framework that accounts for the random phase shifts imparted to the formed echo signals by incorporating the random phase shifts and each sensitivity map into a forward model.