Denoising unidimensional por esparsificação no domínio wavelet

Abstract

A denoising algorithm seeks to remove or reduce noise from signals, and it’s specially used for white noise. For one-dimensional signals, the discrete wavelet transform (DWT) and the short-time Fourier transform (STFT) are the main transformations used in denoising, and both present several parameters that should be selected by the user. Due to the great influence those parameters have on the algorithm’s performance, the proposal of this work is to develop a variation of the DWT denoising (wavelet shrinkage) in which the basis and scale parameters are adapted to maximize the sparsity of the signal’s representation in the wavelet domain. Due to the orthogonality of the transformation, the l1 norm was used as an objective sparsity measure. Two variations of the denoiser were presented, with respect to the number of basis that make up the dictionary. Tests were performed on several signals for a comparison with the time-frequency block denoising in terms of performance and computational cost. The results showed that the proposed techniques presented, on average, higher mean performance than the time-frequency block denoising. With the use of the Wilcoxon non-parametric statistical test, it was concluded that the use of a reduced dictionary does not significantly affect the performance, even with the reduction of the processing time by four times, approximately