Direction-of-arrival (DOA) estimation of speech signals using a set of spatially separated microphones in an array is a problem arising in many practical applications. Examples include human computer interfaces, automatic camera-steering systems for multipartecipant videoconferencing, and tracking systems in smart home environments. This paper introduces a robust method for speech signals localization which makes use of sparsity models for signal representation, and includes an analysis of the denoising problem for realistic applications using MEMS microphone arrays. Experimental results on both synthetic and real speech data show that the proposed method is noise-robust and provides high reliable localization performances even in case of multiple sources and small number of microphones.