A method for signal denoising based on the compressive sensing reconstruction

In this paper we present an approach for signal denoising using compressive sensing (CS) reconstruction algorithm. It has been known that the successful reconstruction of CS signals can be achieved using threshold based algorithm in the Fourier transform domain, based on just a small number of randomly chosen samples. The resulting signal has higher SNR compared to the input signal, which is used as a main premise of the proposed denoising solution. Namely, the signal denoising is done by averaging the reconstructed signal versions obtained in different iterations based on different subsets of random samples. The analysis of output SNR is done is terms of the number of iterations required for successful results. The influence of the number of random samples used in the iterations is analyzed as well. The proposed approach is illustrated on examples.