This paper presents a study on frame-level multi-pitch estimation (MPE) for polyphonic piano music based on sparse representation approach. In this approach, a multi-pitch input spectrum is represented by a sparse linear combination of a large number of spectrum exemplars in a given dictionary. By estimating the sparse weight vector and identifying its non-zero elements, a set of possible pitch candidates can be found. This study is focused mainly on the construction and optimization of the exemplar dictionary. A complete dictionary is first built from single-note piano music. We propose to perform prescreening on the dictionary by which the exemplars of the notes belonging to certain octaves and chromas are excluded during the subsequent estimation. Experimental results show that the pre-screening process not only helps in reducing the computational complexity, but also leads to more accurate pitch estimation. On the formulation of sparse estimation problem, we introduce a probabilistic assumption on the estimation error, such that the estimation is converted into a constrained convex quadratic programming problem. We also propose to use spectral combination as a new scheme of pitch determination from the estimated sparse weights.
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