Here, the coefficient vector is assumed to be a sparse vector. Then, the time-dependent coefficient vector of the POD modes is determined by minimizing the difference between the time-series pressure data and the reconstructed pressure at the optimal points. Based on the POD modes, the points that effectively represent the features of the pressure distribution are optimally placed by the sensor optimization technique. In this study, the proper orthogonal decomposition (POD) mode calculated from the time-series PSP data is used as a modal basis. We propose a noise reduction method for unsteady pressure-sensitive paint (PSP) data based on modal expansion, the coefficients of which are determined from time-series data at optimally placed points.
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