  The synthesis of sound via deep learning methods has recently received much
attention. Some problems for deep learning approaches to sound synthesis relate
to the amount of data needed to specify an audio signal and the necessity of
preserving both the long and short time coherence of the synthesised signal.
Visual time-frequency representations such as the log-mel-spectrogram have
gained in popularity. The log-mel-spectrogram is a perceptually informed
representation of audio that greatly compresses the amount of information
required for the description of the sound. However, because of this
compression, this representation is not directly invertible. Both signal
processing and machine learning techniques have previously been applied to the
inversion of the log-mel-spectrogram but they both caused audible distortions
in the synthesized sounds due to issues of temporal and spectral coherence. In
this paper, we outline the application of a sinusoidal model to the inversion
of the log-mel-spectrogram for pitched musical instrument sounds outperforming
state-of-the-art deep learning methods. The approach could be later used as a
general decoding step from spectral to time intervals in neural applications.
