In underwater acoustics, inversion tech- niques, also called "Matched Field" processing, remain the best methods for locating acoustic sources. But this is without counting on the environmental parameter fluctuations that lead to injurious coherence loss. We have shown in a previous work that a sub-antenna approach could be well suited to deal with such coher- ence loss, however at the expense of a lower resolution. In this paper, we propose to solve this drawback by considering sparse priors. In the experimental part of this paper, by using numerical simulations of plane waves subject to coher- ence loss, we demonstrate that the proposed method not only outperforms a classical beamformer in terms of source localization performance, but also, that it improves the antenna resolution.