Provided are apparatus and methods for forming a multidimensional image of inanimate or animate objects which utilize a magnetization source (112) to magnetize a volume of an object to be imaged, a radiation source (118) for applying a radiation field to the object to be imaged, an output signal detector (120) for producing output signals in response to the secondary radiation at a plurality of spatial locations outside of the object as a function of time, processors (126, 126a and 126b) for determining a plurality of Fourier components, for associating the Fourier components due to each voxel (14) by phase, and for converting each set of components into a voxel location, and an image processor (128) for producing an image.