基于投影多元奇异谱分析的压敏漆时间序列图像去噪
Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis
摘要：
时间序列数据，如不稳定的压敏漆（PSP）测量数据，可能包含大量的随机噪声。因此，在这项研究中，我们研究了一种降噪方法，结合多元奇异谱分析（MSSA）与低维数据表示。MSSA是一种状态空间重构技术，利用时间延迟嵌入，低维表示是通过将数据投影到奇异值分解（SVD）的基础上实现的。所提出的方法对非定常PSP数据的降噪性能，即，的投影MSSA，与截断SVD方法，最常用的降噪方法之一。结果表明，投影MSSA方法比截断SVD方法具有更好的降噪性能。此外，与截断SVD方法相比，投影MSSA的性能对截断秩不太敏感。此外，投影MSSA通过从噪声输入数据中提取状态空间中的平滑轨迹来有效地实现去噪。预计，预计MSSA将是有效的，以减少随机噪声，不仅在PSP的测量数据，但也各种高维时间序列数据。
英文摘要：
Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum analysis (MSSA) with low-dimensional data representation. MSSA is a state-space reconstruction technique that utilizes time-delay embedding, and the low-dimensional representation is achieved by projecting data onto the singular value decomposition (SVD) basis. The noise-reduction performance of the proposed method for unsteady PSP data, i.e., the projected MSSA, is compared with that of the truncated SVD method, one of the most employed noise-reduction methods. The result shows that the projected MSSA exhibits better performance in reducing random noise than the truncated SVD method. Additionally, in contrast to that of the truncated SVD method, the performance of the projected MSSA is less sensitive to the truncation rank. Furthermore, the projected MSSA achieves denoising effectively by extracting smooth trajectories in a state space from noisy input data. Expectedly, the projected MSSA will be effective for reducing random noise in not only PSP measurement data, but also various high-dimensional time-series data.
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