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Musical noise often arises in the outputs of time-frequency binary mask based blind source separation approaches. Post-processing is desired to enhance the separation quality. An efficient musical noise reduction method by time-domain sparse filters is presented using convex optimization. The sparse filters are sought by L1 regularization and the split Bregman method. The proposed musical noise reduction method is evaluated by both synthetic and room recorded speech and music data, and found to outperform existing musical noise reduction methods in terms of the objective and subjective measures.