Like rhythm and timbre, pitch as a mid-level music feature holds the promise of bridging the well-known semantic gap between low-level features and high-level semantics of music. Pitch estimation is an important first step towards this ultimate goal. In this thesis, we target the extraction of multiple pitch contours from piano music signals. Specifically, the pitch estimation is formulated as a sparse representation problem, in which the feature vector of a piano music segment (or frame) is represented as a linear combination of the feature vectors of individual piano notes. The note candidates of the input piano music segment are determined according to the harmonic structure of piano sounds. Then, the sparse representation problem is solved by l1-regularized minimization. A post-processing method based on hidden Markov models (HMMs) is applied to the resulting sparse vector for accuracy refinement. The system performance is evaluated using l1 classical music recordings of a real piano. The results show that the proposed system outperforms three state-of-the-art systems.