In this paper, we propose a single-channel speech enhancement system based on the noise robust exemplar matching (N-REM) framework using coupled dictionaries. N-REM approximates noisy speech segments as a sparse linear combination of speech and noise exemplars that are stored in multiple dictionaries based on their length and associated speech unit. The dictionaries providing the best approximation of the noisy mixtures are used to estimate the speech component. We further employ a coupled dictionary approach that performs the approximation in the lower dimensional mel domain to benefit from the reduced computational load and better generalization, and the enhancement in the short-time Fourier transform (STFT) domain for higher spectral resolution. The proposed enhancement system is shown to have superior performance compared to the exemplar-based sparse representations approach using fixed-length exemplars in a single overcomplete dictionary.