Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis

TL;DR

This paper introduces a projected multivariate singular spectrum analysis method that effectively reduces random noise in high-dimensional time-series data, outperforming traditional truncated SVD, especially in unsteady pressure-sensitive paint measurements.

Contribution

The study proposes a novel noise-reduction technique combining MSSA with low-dimensional SVD projection, demonstrating improved performance and robustness over existing methods.

Findings

Projected MSSA outperforms truncated SVD in noise reduction.

The method is less sensitive to truncation rank.

Effective in denoising high-dimensional time-series data.

Abstract

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.