MULTIVARIATE SERIES NOISE REDUCTION VIA SEQUENTIAL MOJORIZATION METHOD AND ITS EXTENSIONS

摘要

Based on the Hankel structured low-rank approximation and the technique of majorization, the sequential majorization method (SMM-Cadzow) proposed by Qi et al. (2018) has been proven to be an effective and fast method for the signal extraction from noisy time series. This method elevates the approximation of low-rank matrix by designing a new object function. In this paper, we use the idea of multivariate analysis to reconstruct the SMM-Cadzow method and therefore form the multivariate version of SMM-Cadzow (MSMM-Cadzow). We thoroughly describe the problems of selecting two important parame-ters (window length and the rank of the low-rank matrix). The result of signal extraction largely depends on the two parameters. The condition which perfectly fits the MSMM-Cadzow model is also introduced in the paper. Focusing on denoising the weak signal, we propose two new schemes (recycling MSMM algorithm and variate accumulation MSMM algorithm) using the MSMM-Cadzow. The numerical results demonstrated that MSMM-Cadzow has a significant importance on signal extraction and the denoising of weak signal has been improved by the proposed algorithms (recycling MSMM algorithm and variate accumulation MSMM algorithm).