Recently a progress in computational imaging has been noticed with the potential to improve the capabilities of millimeter-wave imaging systems. In this paper, an interferometric synthetic aperture systems is considered to be the conventional approach to image reconstruction that, in order to overcome its cost limitations and system complexity, both hardware and digital post-processing solutions are offered. A passive multiplexing cavity is added to encode received signals into the physical layer helping to reduce the number of measurement ports and thus the active RF chains without affecting the initial number of receiving antennas. This proposed technique leads to inverse problem solving process. A novel numerical method is then developed, based on a matrix formalism yielding a mathematical description of the computational approach. A numerical study is therefore performed to approve the feasibility of this technique for a better image reconstruction followed by an experimental study carried out at 92 GHz as a proof of concept.