A principal component-based algorithm for denoising in single channel data (PCA for denoising in single channel data)

A denoising technique for single channel data is proposed. By assuming the observed signal to be the mixture of two unknown uncorrelated sources, an expression for the principal components (PC) of the set constituted by the signal and its k-sample delayed version is derived. The expression does not require matrix manipulations and may be hence useful when both speed and memory usage are crucial. The second PC was found to be a suitable estimate of one of the sources. Illustrations are provided for a simulated voltage signal corrupted by harmonics and transient disturbances as well as for a real electromyographic signal with electrocardiographic interference. A comparison with a standard, wavelet-based method for denoising is also provided.