In recent work we showed the interest of using sparse representation techniques to estimate a target scene observed by wideband radar systems. However the principle was demonstrated in a white noise background only. In this paper, we present an extended version of our sparse estimation technique that attempts to take into account the (possible) presence of diffuse clutter. More specifically, an autoregressive model is considered for the noise vector. Performance of the technique is studied on synthetic and experimental data. Pertinence of the noise model is discussed.