Sparse representations have previously been applied to the automatic music transcription (AMT) problem. Structured sparsity, such as group and molecular sparsity allows the introduction of prior knowledge to sparse representations. Molecular sparsity has previously been proposed for AMT, however the use of greedy group sparsity has not previously been proposed for this problem. We propose a greedy sparse pursuit based on nearest subspace classification for groups with coherent blocks, based in a non-negative framework, and apply this to AMT. Further to this, we propose an enhanced molecular variant of this group sparse algorithm and demonstrate the effectiveness of this approach.

Non-negative Matrix Factorisation (NMF) is a popular tool in musical signal processing. However, problems using this methodology in the context of Automatic Music Transcription (AMT) have been noted resulting in the proposal of supervised and constrained variants of NMF for this purpose. Group sparsity has previously been seen to be effective for AMT when used with stepwise methods. In this paper group sparsity is introduced to supervised NMF decompositions and a dictionary tuning approach to AMT is proposed based upon group sparse NMF using the β-divergence. Experimental results are given showing improved AMT results over the stateof-the-art NMF-based AMT system

Abstract-Automatic Music Transcription (AMT) can be performed by deriving a pitch-time representation through decomposition of a spectrogram with a dictionary of pitch-labelled atoms. Typically, Non-negative Matrix Factorisation (NMF) methods are used to decompose magnitude spectrograms. One atom is often used to represent each note. However, the spectrum of a note may change over time. Previous research considered this variability using different atoms to model specific parts of a note, or large dictionaries comprised of datapoints from the spectrograms of full notes. In this paper the use of subspace modelling of note spectra is explored, with group sparsity employed as a means of coupling activations of related atoms into a pitched subspace.Stepwise and gradient-based methods for non-negative group sparse decompositions are proposed. Finally, a group sparse NMF approach is used to tune a generic harmonic subspace dictionary, leading to improved NMF-based AMT results.

Musical signals can be thought of as being sparse and structured, with few elements active at a given instant and temporal continuity of active elements observed. Greedy algorithms such as Orthogonal Matching Pursuit (OMP), and structured variants, have previously been proposed for Automatic Music Transcription (AMT), however some problems have been noted. Hence, we propose the use of a backwards elimination strategy in order to perform sparse decompositions for AMT, in particular with a proposed alternative sparse cost function. However, the main advantage of this approach is the ease with which structure can be incorporated. The use of group sparsity is shown to give increased AMT performance, while a molecular method incorporating onset information is seen to provide further improvements with little computational effort.

Automatic Music Transcription (AMT) seeks to understand a musical piece in terms of note activities. Matrix decomposition methods are often used for AMT, seeking to decompose a spectrogram over a dictionary matrix of note-specific template vectors. The performance of these methods can suffer due to the large harmonic overlap found in tonal musical spectra. We propose a row weighting scheme that transforms each spectrogram frame and the dictionary, with the weighting determined by the effective correlations in the decomposition. Experiments show improved AMT performance.