Improved Wavelet Denoising by Non-Convex Sparse Regularization Under Double Wavelet Domains

This paper presents a double wavelet denoising (DWAD) method, which can preserve more details of an original signal. Although the noise removal method based on wavelet transform has been widely used, it still performs poorly for the signals with a low signal-to-noise ratio (SNR) or frequency overlap. Different from the wavelet denoising methods based on a single basis function, the DWAD considers filtering the wavelet coefficients of the noisy signal by threshold functions under two different wavelet domains, simultaneously. It considers using the difference of wavelet coefficient distribution and forcing the denoised signals under two wavelet domains to be the same to achieve more retention of details. In addition, the arctangent function is employed as a penalty function for wavelet coefficients to induce strong sparse wavelet coefficients. The DWAD is applied to one-dimensional signals and it is found that some wavelet coefficients which are smaller than the threshold could be retained during noise removal. The experiment results show that the average SNR of different noise levels is improved by at least 4.2 and 2.1 dB compared with the classical soft threshold method for the one-dimensional and image signals, respectively. Besides, the DWAD tends to obtain better performance on the details of original signals.