Speech enhancement is one of the many challenging tasks in signal processing, especially in the case of nonstationary speech-like noise. In this paper a new incoherent discriminative dictionary learning algorithm is proposed to model both speech and noise, where the cost function accounts for both “source confusion” and “source distortion” errors, with a regularization term that penalizes the coherence between speech and noise sub-dictionaries. At the enhancement stage, we use sparse coding on the learnt dictionary to find an estimate for both clean speech and noise amplitude spectrum. In the final phase, the Wiener filter is used to refine the clean speech estimate. Experiments on the Noizeus dataset, using two objective speech enhancement measures: frequency-weighted segmental SNR and Perceptual Evaluation of Speech Quality (PESQ) demonstrate that the proposed algorithm outperforms other speech enhancement methods tested.