A New Method for Sparse Signal Denoising Based on Compressed Sensing

Whether it is classic filter denoising, Fourier transform denoising, or the emerging wavelet transform denoising, a common characteristic is that denoising is only limited to some transform field. Also, these denoising methods are influenced greatly by the change of signal parameters, such as frequency, amplitude, etc. In order to effectively overcome the above-mentioned shortcomings of these denoising methods, this paper first introduces the basic principle of compressed sensing, and proposes a new compressed sensing denoising method to eliminate the noise in sparse signal according to the relationship between compressed sensing and signal sparsity. Then, the basic idea and algorithm steps of the new method is given, and an improved algorithm with better denoising effect is proposed aiming at the peak distortion produced by compressed sensing denoising method. At last, the denoising effect of the new method is validated by simulation experiment.