A magnetic resonance imaging system may include: a magnet; gradient coils; an RF pulse transmitter; an RF receiver that receives MR signals from tissue that has been exposed to RF pulses from the RF pulse generator, gradient fields from the gradient coils, and a magnetic field from the magnet; a system controller that controls the magnet, gradient coils, RF pulse transmitter, and RF receiver so as to generate data representative of at least a portion of the composition of an object, including controlling the gradient coils and RF receiver so as to cause MRI data to be acquired that includes information about at least one attribute of the object at different points in time and that represents an incomplete sample of a portion of k-space that is a Fourier transform of the object; and a data processing system that generates one or more images of at least a portion of the object based on the MRI data.