用最优传输融合多谱图,实现时间频率分辨率的超分辨率提升。
Enhancing time-frequency resolution with optimal transport and barycentric fusion of multiple spectrogram

- 通过最优传输计算多谱图的巴氏中心,生成高分辨谱图。
- 在合成信号和语音数据上优于现有无监督融合方法。
- 支持任意网格设置,计算效率更高,适合信号分析场景。
时频表示(如短时傅里叶变换,STFT)是分析非平稳信号的基础工具,但其时间与频率的定位精度受限于伽柏-海森堡不确定性原理。本文提出一种通过融合多个不同分辨率的谱图生成超分辨率谱图的方法。具体地,利用最优传输(OT)散度计算输入谱图的巴氏中心作为超分辨率谱图。该方法无需输入谱图共享相同的时间-频率网格,可使用任意STFT参数生成,并在用户指定的任意网格上定义结果。研究了基于不同运输成本的多种OT散度,提出一种新运输成本,在保持时间-频率几何结构的同时显著降低计算复杂度。采用非平衡最优传输框架,推导出新的块极大极小算法以高效计算巴氏中心。在受控合成信号和真实语音数据上进行了定量与定性评估,结果表明该方法能结合输入谱图的最佳定位特性,性能优于当前最先进的无监督融合方法。
原文摘要 · Abstract (English)
Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp localization in both time and frequency is inherently limited by the Gabor-Heisenberg uncertainty principle. In this paper, we address this limitation by introducing a method to generate super-resolution spectrograms through the fusion of two or more spectrograms with varying resolutions. Specifically, we compute the super-resolution spectrogram as the barycenter of input spectrograms using optimal transport (OT) divergences. Unlike existing fusion approaches, our method does not require the input spectrograms to share the same time-frequency grid. Instead, the input spectrograms can be computed using any STFT parameters, and the resulting super-resolution spectrogram can be defined on an arbitrary user-specified grid. We explore various OT divergences based on different transportation costs. Notably, we introduce a novel transportation cost that preserves time-frequency geometry while significantly reducing computational complexity compared to standard Wasserstein barycenters. We adopt the unbalanced OT framework and derive a new block majorization-minimization algorithm for efficient barycenter computation. We validate the proposed method on controlled synthetic signals and recorded speech using both quantitative and qualitative evaluations. The results show that our approach combines the best localization properties of the input spectrograms and outperforms an unsupervised state-of-the-art fusion method.
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