An innovative multi-level singular value decomposition and compressed sensing based framework for noise removal from heart sounds

Heart sounds have attracted increasing attentions resulting from the correlation with cardiac mechanical activity. Nevertheless, the interferences caused by broadband noise have an influence on the further processing and analyzing of heart sounds. This paper presents an innovative denoising framework based on a joint combination of modified singular value decomposition (SVD) and compressed sensing (CS) in order to solve this problem. Firstly, the modified SVD is proposed to process the raw heart sounds, and it aims to separate the heart sound components from the noise components as many as possible by multi-level decomposition and reconstruction, named multi-level SVD. Then, the CS based denoising is applied to further elimination of the noise remaining after the multi-level SVD operation through sparse reconstruction. The performance of proposed framework is evaluated qualitatively and quantitatively, including the test and verification in terms of several standard metrics, and the comparison with the widely used denoising methods such as wavelet transform (WT) and empirical mode decomposition (EMD) using the heart sound databases in different noise levels. The results show that the denoising framework not only improves the signal quality but also preserves the original morphological characteristics of heart sounds, which corresponds to a higher signal-to-noise ratio (SNR), a smaller mean square error (MSE) and a higher correlation coefficient between the denoised signal and original signal. It indicates that the denoising framework can remove the noise and maintain the original physiological and pathological information of heart sounds effectively. This suggests that the denoising framework has potentially theoretical and applied value in heart sounds denoising as well as the future applications of other biomedical signals denoising.