Variational Inference of Structured Line Spectra Exploiting Group-Sparsity
- Wed, Mar 01, 2023
We developed a variational Bayesian inference algorithm for structured line spectra that actively exploits the structure that naturally occurs in many applications to improve estimation performance. For example, consider the audio signal produced by several notes played together in a chord. Each note is a line spectrum with a harmonic structure, i.e. each line is at a multiple of some fundamental frequency - the pitch of the note. When several notes are played together, the result is a linespectrum that is a mixture of several harmonic spectra. By explicitly considering the structure in each harmonic spectrum, our proposed method is able to outperform state-of-the-art multi-pitch estimation methods on the Bach-10 dataset, even machine learning methods pre-trained on the instruments in the dataset. An example of the detected pitch for several seconds of the chorale “Ach Gott und Herr” from the dataset is shown in the figure. Structured line spectra occur (approximately) in many other applications, such as the detection and estimation of extended objects using radar signals or variational mode decomposition. In both examples, we were able to outperform other state-of-the-art algorithms, demonstrating the versatility of the developed method.
This work has been submitted to IEEE Transactions on Signal Processing. If you are interested have a look at the arxiv preprint.
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