Several studies have pointed out the need of mid-level representations of music signals for information retrieval and signal processing applications. In this paper, we investigate a new representation based on sparse decomposition of the signal into a collection of instrument-specific harmonic atoms modelling notes of various pitches played by different instruments. Each atom is composed of windowed harmonic sinusoidal partials whose amplitudes are learned on a training database. An efficient Matching Pursuit algorithm was designed to extract the best atoms and to estimate the phases of their partials. Then we explain how the resulting representation can be exploited for automatic instrument recognition. Preliminary experiments on a test database of solo excerpts show promising results.