Advances in compressed sensing (CS) theory have brought new perspectives to encoding and decoding of signals with sparse representations. The encoding strategies are determined by measurement matrices whose design is a critical aspect of the CS applications. In this study, we propose a novel measurement matrix design methodology for direction of arrival estimation that adapts to the prior probability distribution on the source scene, and we compare its performance over alternative approaches using both on-grid and gridless reconstruction methods. The proposed technique is derived in closed-form and shown to provide improved compression rates compared to the state-of-the-art. This technique is also robust to the uncertainty in the prior source information. In the presence of significant mutual coupling between antenna elements, the proposed technique is adapted to mitigate these mutual coupling effects.