Data recovery of clean signal from highly noisy data: a compressed data fusion approach

Compressed sensing algorithm is used to fuse spatially resolved but noisy full-field data with clean but scattered data to reconstruct full-field clean data. In the applications of flow measurement, control, and monitoring, a particularly challenging task is to recover clean signal from highly noisy data. One commonly used method is low dimensional analysis. For example, proper orthogonal decomposition (POD) is commonly used to extract coherent signal patterns from noisy data. However, with a low signal-to-noise ratio, the selection criteria of the proper POD modes for reconstruction is usually based on subjective observation. In addition, the strong noise can severely distort the mode coefficients. Therefore, POD analysis not only has restriction in the applications of complicated flow phenomena, but also can lead to a low-quality reconstruction. In current method, the two problems are naturally solved by compressed sensing, which is to find the optimal mode coefficients to reconstruct the clean data using the most relevant POD modes. Fabricated patterns and fast PSP measurement pressure fields of wake flows are tested. It shows that current compressed data fusion approach can significantly improve the performance of recovery clean data compared with POD analysis.