This paper proposes an exemplar-based speech enhancement method based on high-resolution STFT magnitude spectrograms, where a selection of the nonnegative training data is used as the dictionary to provide a holistic nonnegative representation of the test data. We discuss how this exemplar-based model ensures that the enhanced speech signal falls on the speech manifold, which improves the quality of the enhanced speech signal. To exploit the temporal continuity, a vector autoregressive model is used to model the activations where the model parameters are learned using a new NMF-based approach. Results from several supervised and semi-supervised speech enhancement experiments indicate that the proposed exemplar-based method outperforms the considered supervised and unsupervised denoising algorithms in terms of both segmental SNR and PESQ at different input SNRs.