We present a convex optimization technique for unmixing lung sounds to improve computer-aided pulmonary auscultation. An auscultatory sound of a patient with pulmonary disorder may be composed of continuous and discontinuous adventitious sounds as well as breath. Our technique exploits sparse and low-rank properties of these sounds in the Fourier, wavelet, and time-frequency domains, which can be quantified as convex functions. The optimization algorithm is derived from the alternating direction method of multipliers (ADMM). This approach enables the lung sound unmixing without training data for learning diverse structures of lung sounds in time-frequency domains. We show some experimental examples and discuss further improvements.