A noninvasive medical diagnostic technique by quantitative three-dimensional imaging of dielectric permittivity is proposed. Dielectric image of a target is reconstructed by measuring the microwave scattering field and utilizing a scattering matrix inversion algorithm. It is expected to yield a resolution limited only by signal-to-noise ratio, and not by the wavelength or diffraction. The microwave dose will be in the order of microwatt per gram to tens of microwatt per gram, which is two to three orders of magnitude below the safety level. Owing to the sensitivity of dielectric permittivity with respect to various biological tissues, the system will, comparing to existing imaging devices, provide higher contrast between soft tissues and between tumor and normal tissues. Wavelength places a limit on resolution only in the case where some far-field approximation is used for the scattering field. To overcome the wavelength limitation and to retrieve all three dimensions of the target profile, our approach is to convert the scattering equation to a scattering matrix form without neglecting higher order terms. In order to stabilize the matrix inversion, scattering data in the near zone are employed and a least-mean-square algorithm is devised to reconstruct the target.