AI 中文总结
针对自适应Chirplet变换实际部署的挑战，本文引入单位归一化和残差投影消除发散，采用混合CPU - GPU架构及多通道批处理实现加速，引入分层搜索降低内存使用，为基于Chirplet的信号分解奠定稳定可部署基础。
AI 中文摘要
自适应Chirplet变换是一种能将非平稳信号分解为稀疏Chirplet的灵活框架，已应用于脑电、肌电和雷达等信号。但其实际部署受算法不稳定和高维参数空间搜索计算成本两大挑战阻碍。本文通过一系列贡献解决了这些问题。首先引入单位归一化和基于残差的投影，使其分解符合匹配追踪理论，消除发散并大幅降低残差误差。采用混合CPU - GPU架构，将Chirplet族生成卸载到CPU，在GPU上并行搜索，实现加速。多通道批处理可同时处理多信号，进一步放大加速效果。最后引入分层粗到细搜索，降低峰值内存使用。这些贡献为基于Chirplet的信号分解建立了正确、稳定且可实际部署的基础。
英文摘要
The Adaptive Chirplet Transform is a flexible framework that can decompose non-stationary signals into sparse chirplets; it has been applied to signals such as electroencephalography, electromyography and radar. However, the practical deployment of this transform has been hindered by two challenges: algorithmic instability in prior implementations, which can lead to divergent decompositions, and the computational cost of searching over a high-dimensional parameter space. This paper addresses both by a sequence of contributions. Firstly, unit normalization and residual-based projection are introduced to align the decomposition with Matching Pursuit Theory, thereby eliminating divergence and substantially reducing residual error across all signal domains, as demonstrated on three representative signal types. A hybrid CPU-GPU architecture offloads chirplet family generation to the CPU while parallelizing the search on the GPU, removing bottlenecks in CPU-only search and GPU-only generation, achieving speedups of 6.6-7.38x on desktop hardware, with consistent gains observed across laptop and embedded platforms. Multichannel batching enabled simultaneous multi-signal processing, amplifying the speedup, which scaled from 3.94x for a single channel to 8.22x at 10 channels. Finally, a hierarchical coarse-to-fine search, inspired by Logon Expectation Maximization, is introduced. This reduced peak memory usage below 1 GB while maintaining similar reconstruction quality, at the cost of longer runtime. Together, these contributions establish a correct, stable and practically deployable foundation for chirplet-based signal decomposition. Index Terms: Chirplet Transform, GPU Computing, Matching Pursuit, Signal Decomposition, Sparse Representation, Time-Frequency Analysis
Comments13 pages, 8 figures. Under submission at the Open Journal of Signal Processing. A reference implementation of the adaptive chirplet transform algorithm is available at https://github.com/nishantkumar201/adaptive-chirplet-transform
