This paper investigates sub-THz computational imaging using compact, wideband, cavity-backed frequency-diverse antennas fabricated through silicon micromachining techniques. This paper presents a forward model based on pseudo-random frequency-diverse patterns using a Mills-Cross transmitter and receiver pair, which provides high-resolution imaging capabilities in the 220-330 GHz frequency range. The model is coupled with advanced compressed sensing algorithms, specifically Compressive Sampling Matching Pursuit (CoSaMP) and Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), to enhance imaging performance under limited data acquisition. Through emulated simulation and experimental data, it is demonstrated that the system's ability to achieve range resolutions down to 1.4 mm and angular resolutions of 0.35°, even in the presence of noise, and analyze the trade-off between computational complexity and imaging accuracy. Sparsity investigations in spatial antenna population and frequency samples are comprehensively explored in this paper. The results show that using only 6.7% of the data, the CoSaMP algorithm can reconstruct a discernable image of the “KTH” logo. Results show that CoSaMP provides lower reconstruction error for sparse target distributions, while FISTA achieves superior noise resilience. The study highlights the practical implications of using frequency-diverse antennas in security screening and industrial inspection, where high-resolution imaging at sub-THz frequencies is demanded.