Sparse wavefield reconstruction and denoising with boostlets

TL;DR

This paper introduces boostlets, a new spatiotemporal representation system that achieves sparser wavefield decompositions than existing methods, leading to improved denoising performance in wavefield analysis.

Contribution

The paper presents boostlets, a novel framework for sparse wavefield decomposition that outperforms wavelets and shearlets in sparsity and denoising effectiveness.

Findings

Boostlets produce significantly sparser decompositions.

Boostlet-based denoising outperforms traditional methods.

Boostlets provide a unified space-time wavefield representation.

Abstract

Boostlets are spatiotemporal functions that decompose nondispersive wavefields into a collection of localized waveforms parametrized by dilations, hyperbolic rotations, and translations. We study the sparsity properties of boostlets and find that the resulting decompositions are significantly sparser than those of other state-of-the-art representation systems, such as wavelets and shearlets. This translates into improved denoising performance when hard-thresholding the boostlet coefficients. The results suggest that boostlets offer a natural framework for sparsely decomposing wavefields in unified space-time.