1. A method of constructing a 3-dimensional nuclear magnetic resonance image of at least a portion of a target without generating gradients in a static magnetic field, comprising: a) relying upon environmentally innate static magnetic field gradients and using a plurality of magnetic field generating coils with spatially distinct magnetic field patterns, transmitting alternating magnetic field pulses at the Larmor frequency of the target using a plurality of linearly independent combinations of relative current amplitudes and/or phases among the transmitting coils, and using P different values of total transmitted energy for each combination of transmit coils used, where P>1; b) using a plurality of magnetic field receiving coils with spatially distinct magnetic field patterns, detecting and recording a set of nuclear magnetic resonance signals arising from each transmit pulse, each of the set of nuclear magnetic resonance signals comprising a plurality of samples; c) arranging the set of recorded nuclear magnetic resonance data samples as a vector b; and d) reconstructing a 3-dimensional nuclear magnetic resonance image wherein each sampled location in the 3-dimensional image space is assigned a scalar value s, wherein the scalar value s is computed as a weighted linear combination of the recorded data samples b: s=Σ j w j b j