Sparse wavefield reconstruction and denoising with boostlets

2025-02-12

AI Summary

This study addresses the challenge of sparse reconstruction and denoising of non-dispersive wavefields. We propose a novel spatiotemporal basis function—termed *boostlet*—specifically designed to match the physical propagation characteristics of such waves. The boostlet achieves localized, adaptive wavefront representation via scale dilation, hyperbolic rotation, and translation, marking the first incorporation of relativistic boost transformations into signal sparse representation. Compared with conventional bases (e.g., wavelets, shearlets), boostlets yield significantly improved sparsity and structural fidelity. Leveraging this basis, we develop a joint spatiotemporal sparse coding framework coupled with hard-thresholding, which simultaneously enhances reconstruction accuracy and noise suppression—achieving superior signal-to-noise ratio (SNR) performance. Experimental results validate the effectiveness and state-of-the-art capability of the boostlet-based framework as a unified spatiotemporal sparse representation system.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Sparse wavefield reconstruction using boostlets.
• Boostlets outperform wavelets in sparsity.
• Boostlets enhance denoising via hard-thresholding.

Innovation

• Boostlets decompose wavefields sparsely
• Boostlets outperform wavelets and shearlets
• Boostlets enhance denoising via hard-thresholding