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A Continuous Boostlet Transform for Acoustic Waves in Space-time by Zea, Elias; Laudato, Marco; Andén, Joakim is a scholarly article available to read on EtoBox.

What is A Continuous Boostlet Transform for Acoustic Waves in Space-time about?

Sparse representation systems that encode the signal architecture have had an exceptional impact on sampling and compression paradigms. Remarkable examples are multi-scale directional systems, which, similar to our vision system, encode the underlying architecture of natural images with sparse features. Inspired by this philosophy, the present study introduces a representation system for acoustic waves in 2D space-time, referred to as the boostlet transform, which encodes sparse features of natural acoustic fields with the Poincar\'e group and isotropic dilations. Continuous boostlets, $\psi_{a,\theta,\tau}(\varsigma) = a^{-1} \psi \left(D_a^{-1} B_\theta^{-1}(\varsigma-\tau)\right) \in L^2(\mathbb{R}^2)$, are spatiotemporal functions parametrized with dilations $a > 0$, Lorentz boosts $\theta \in \mathbb{R}$, and translations $\smash{\tau \in \mathbb{R}^2}$ in space--time. The admissibility condition requires that boostlets are supported away from the acoustic radiation cone, i.e., have phase velocities other than the speed of sound, resulting in a peculiar scaling function. The continuous boostlet transform is an isometry for $L^2(\mathbb{R}^2)$, and a sparsity analysis with expe

Author

Zea, Elias; Laudato, Marco; Andén, Joakim

Published

2024

Language

EN