An improved multivariate wavelet denoising algorithm combined with subspace and principal component analysis is presented in this paper. The key element is deriving an optimal orthogonal matrix that can project the multivariate observation signal to a signal subspace from observation space. Univariate wavelet shrinkage operator is then applied to the projected signals channel-wise resulting in the improvement of the output SNR. Finally, principal component analysis is performed on the denoised signal in the observation space to further improve the denoising performance. Experimental results based on synthesized and real world ECG data verify the effectiveness of the proposed algorithm.

The dyadic filter bank property of multivariate empirical mode decomposition (MEMD) for white Gaussian noise (WGN) is well established. In order to investigate the way MEMD behaves in the presence of fractional Gaussian noise (fGn), we conduct thorough numerical experiments for MEMD for fGn inputs. It turns out that similar to WGN, MEMD follows dyadic filter bank structure for fGn inputs, which is more stable than empirical mode decomposition (EMD) regardless of the Hurst exponent. Moreover, the estimation of the Hurst exponent of fGn contaminated with different kinds of signals is also presented via MEMD in this work.