In this talk, Elias will give an overview of the recently introduced boostlet transform for wave-based acoustic signal processing in space-time. Boostlets are affine wavelets parametrized by the Weyl group using dilations, Lorentz boosts, and translations. In acoustical terms, boostlets are wave-like functions with a variable frequency and phase speed spectrum, providing a unified treatment of trace waves in space and time.

The talk will begin with the boostlet theory and its physical motivation, in the continuous and discrete settings. After that, Elias will present applications of boostlet frames in wavefield segmentation, as well as sparse reconstruction and denoising, comparing their performance with that of previous multi-scale methods such as wavelets, curvelets, and wave atoms. If time allows, Elias will also demonstrate the emergence of a waveform continuum from the uncertainty principles of the transform. Such a continuum spans waveforms of localized, band-limited, and global nature using Gaussian-parametrized functions of frequency and phase speed. Remarkably, certain classical solutions to the wave equation appear to be recovered from the standard deviation asymptotics of these Gaussians.

(The talk will be in English.)

Elias Zea Marcano is an Assistant Professor of Engineering Acoustics at KTH Royal Institute of Technology in Stockholm, working at the Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL). His research spans noise source separation, aeroacoustics, and room acoustics, with a focus on sparse signal processing and data-driven methods. 

Link to Elias' academic profile.