Denoising of signals and noise extraction by sparse autoregression

Abstract

Denoising is the process of removing noise of a noise contaminated signal, noise extraction is to destill out noise. This can be done by using autoregressive (AR) filters, if the signal was generated by an AR process and if the AR coefficients are known. We introduce a sparse AR denoising/noise extraction method by using Yule-Walker (YW) equations in combination with l1-regularization and compare the results with a ‘classical’ YW based denoising/noise extraction. Simulations show that the novel approach is superior compared to the classical one for short sparse AR signals. The novel approach does not require AR order estimation and may be useful for supervised or automated denoising/noise extraction of sparse AR signals.