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arXiv 1609.09799stat.MLcs.LGcs.SD
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最佳光谱传输及其在音乐转录中的应用

Optimal spectral transportation with application to music transcription

Université Côte d’Azur(蔚蓝海岸大学);CNRS(法国国家科学研究中心);OCA(蔚蓝海岸天文台);IRIT(图卢兹计算机科学研究所);Université de Bretagne Sud(南布列塔尼大学);IRISA(法国国家信息与自动化研究所-雷恩第一大学联合研究中心);Aix-Marseille Université(艾克斯-马赛大学);LIF(计算机科学实验室)

Rémi Flamary, Cédric Févotte, Nicolas Courty, Valentin Emiya

摘要:

许多光谱解混方法依赖于光谱数据到光谱模板字典上的非负分解。特别地,现有技术的音乐转录系统将输入信号的谱图分解到代表性音符谱的字典上。用于量化分解充分性的典型拟合度量是按频率比较数据和模板条目。因此,能量从一个频率箱到另一个频率箱的小位移以及木材的变化可能会损害拟合。我们解决这些问题,通过最佳的运输,并提出了一个新的措施,以适应整体的频率分布的能量,而不是频率明智的。基于声音的谐波性质,新的测量对于能量到谐波相关频率的移位以及能量的小的和局部的位移是不变的。配备了这种新的适应措施,笔记模板的字典可以大大简化为一组狄拉克向量位于目标基频(音高值)。这反过来又为一个非常快速和简单的分解算法提供了基础,该算法可以在真实的音乐数据上实现最先进的性能。

英文摘要:

Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to quantify the adequacy of the decomposition compare the data and template entries frequency-wise. As such, small displacements of energy from a frequency bin to another as well as variations of timber can disproportionally harm the fit. We address these issues by means of optimal transportation and propose a new measure of fit that treats the frequency distributions of energy holistically as opposed to frequency-wise. Building on the harmonic nature of sound, the new measure is invariant to shifts of energy to harmonically-related frequencies, as well as to small and local displacements of energy. Equipped with this new measure of fit, the dictionary of note templates can be considerably simplified to a set of Dirac vectors located at the target fundamental frequencies (musical pitch values). This in turns gives ground to a very fast and simple decomposition algorithm that achieves state-of-the-art performance on real musical data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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