Abstract: A local gradient coil for use in magnetic resonance imaging provides a system of windings that produces a non-monotonic gradient field. The non-monotonic field provides spatially separate regions experiencing similar gradients and thus does not uniquely identify spatially separate spins. Multiple receiving coils positioned near each of the regions of similar gradient field strength are used to receive the multiple NMR signals. A determination of the sensitivity of these receiving coils may be used to determine the contribution from each spin to the signal produced by each coil thus allowing the superimposed signals to be separated.