1. In a magnetic resonance imaging system which includes a magnet which generates a temporally constant magnetic field through an examination region, a radio frequency pulse controller and transmitter which excite magnetic dipoles in the examination region, and gradient magnetic field coils and a gradient magnetic field controller which generate magnetic field gradient pulses across the examination region such that spatially encoded radio frequency magnetic resonance signals are generated, a receiver which receives and demodulates the radio frequency magnetic resonance signals to produce a series of data lines, and an image memory for storing a reconstructed image representation, the improvement comprising: an algebraic reconstruction processor which operates on an array of data lines with an algebraic reconstruction matrix to at least partially reconstruct the data lines into the reconstructed image representation.