We propose a novel algorithm for source signals estimation from an underdetermined convolutive mixture assuming known mixing filters. Most of the state-of-the-art methods are dealing with anechoic or short reverberant mixture, assuming a synthesis sparse prior in the time-frequency domain and a narrowband approximation of the convolutive mixing process. In this paper, we address the source estimation of convolutive mixtures with a new algorithm based on i) an analysis sparse prior, ii) a reweighting scheme so as to increase the sparsity, iii) a wideband data-fidelity term in a constrained from. We show, through theoretical discussions and simulations, that this algorithm is particularly well suited for source separation of realistic reverberation mixtures. Particularly, the proposed algorithm outperforms state-of-the-art methods on reverberant mixtures of audio sources by more than 2 dB of signal-to-distortion ratio.