Field Image Tomography (FIT) is a fundamental new theory for determining the three-dimensional (3D) spatial density distribution of field emitting sources. The field can be the intensity of any type of field including (i) Radio Frequency (RF) waves in Magnetic Resonance Imaging (MRI), (ii) Gamma radiation in SPECT/PET, and (iii) gravitational field of earth, moon, etc. FIT exploits the property that field intensity decreases with increasing radial distance from the field source and the field intensity distribution measured in an extended 3D volume space can be used to determine the 3D spatial density distribution of the emitting source elements. A method and apparatus are disclosed for MRI of target objects based on FIT. Spinning atomic nuclei of a target object in a magnetic field are excited by beaming a suitable Radio Frequency (RF) pulse. These excited nuclei emit RF radiation while returning to their normal state. The intensity or amplitude distribution of the RF emission field g is measured in a 3D volume space that may extend substantially along the radial direction around the emission source. g is related to the 3D tomography f through a system matrix H that depends on the MRI apparatus, and noise n through the vector equation g=Hf+n. This equation is solved to obtain the tomographic image f of the target object by a method that reduces the effect of noise.