Multi-resolution partial tracking with modified Matching Pursuit

The widely used Matching Pursuit algorithm processes the input signal as a whole, and as such does not build relationships between atoms that are selected at every iteration. For audio signals, variants of this algorithm have been introduced that catch structured sets of atoms (“molecules”) sharing common properties: harmonic relationship, time-frequency proximity. However, they are limited by the use of a single scale, hence a fixed time-frequency resolution, within a molecule. In this study, we propose a modified Matching Pursuit that groups atoms at different scales within a given frequency line, allowing molecules with an optimized time and frequency resolution. Results on simple signals, as well as real audio recordings, show that the extra flexibility provided by multi-resolution comes at a small computational cost.