Denoising biomedical signals via adaptive low-rank matrix representation by singular value decomposition using wavelets

Noise reduction of considerable recorded data, e.g., EEG, PPG signals, is significantly important in biomedical signal processing. Singular value decomposition (SVD) method has shown optimistic results in denoising biomedical dataset of images and signals via dimension reduction. However, a still challenge in SVD approach is to find the low-rank representation of the matrix obtained by matricification of the signal of interest adaptively which retrain the energy in signal subspace and neglect the energy in noise subspace. Here, we develop an adaptive rank estimation by the SVD for denoising purpose based on estimating the noise level σest using the first level detail symmlet-wavelet's coefficients d1. The optimal rank is obtained at the point where the difference between the noisy and the reduced rank dataset is approximately below the estimated noise level. The proposed method has successfully estimated the optimal rank which gives the best denoising performance.