An Algebraic Comparison of Synthetic Aperture Interferometry and Digital Beam Forming in Imaging Radiometry

Digital beam forming (DBF) and synthetic aperture interferometry (SAI) are signal processing techniques that mix the signals collected by an antenna array to obtain high-resolution images with the aid of a computer. This note aims at comparing these two approaches from an algebraic perspective with the illustrations of simulations conducted at microwaves frequencies within the frame of the Soil Moisture and Ocean Salinity (SMOS) mission. Although the two techniques are using the same signals and sharing the same goal, there are several differences that deserve attention. From the algebraic point of view, it is the case for the singular values distributions of the respective modeling matrices which are both rank-deficient but do not have the same sensitivity to the diversity of the array’s elementary antennas radiation patterns. As a consequence of this difference, the level and the angular signature of the reconstruction floor error are significantly lower with the DBF paradigm than with the SAI one.