NASA's Soil Moisture Active Passive (SMAP) satellite mission combines a passive L-band radiometer and an active Synthetic Aperture Radar (SAR) instrument in order to monitor the near-surface soil moisture and freeze-thaw states globally, with a revisit frequency of 2-3 days. SMAP provides three soil moisture products: a high-resolution from the radar, a low-resolution from the radiometer, and an intermediate-resolution from the fusion of the radar and radiometer measurements. Unfortunately, SMAP's SAR instrument halted its transmissions after a short operating period. In order to address this limitation, we introduce a novel post-acquisition computational technique aiming to synthesize the active measurements of SMAP, by exploiting the mathematical frameworks of Sparse Representations and Dictionary Learning. We propose a coupled dictionary learning model which considers joint feature spaces, composed of active and passive images, in order to recover the missing active measurements. We formulate our coupled dictionary learning problem within the context of the Alternating Direction Method of Multipliers. Our experimental results demonstrate the ability of the proposed approach to reconstruct the active measurements, achieving better performance compared to state-of-the-art coupled dictionary learning techniques.