Wavelet modulus maxima denoising of seismic signals based on combined wavelet entropy and correlation

In wavelet modulus maxima denoising algorithms, high-frequency wavelet coefficients are all considered as noises, and the useful information in them is ignored, therefore, modulus maxima pickup points are wrongly selected and the calculated noise variances still contain useful information. To solve these problems, this paper proposed a wavelet modulus maxima denoising algorithm which combines wavelet entropy with correlation. The effective signal location is determined by correlation processing of high-frequency wavelet coefficients. The high-frequency wavelet coefficients on the maximum scale are divided into several small zones, and the interval wavelet entropy is calculated. With the mean value of high-frequency wavelet coefficients in the wavelet entropy maxima interval as noise variance, the threshold value of the maxima scale is calculated according to the formula presented by Donoho in 1995. By comparing locations of the maxima point obtained by comparison the threshold values with locations of the useful information obtained by correlation processing, the modulus maxima of the same position are retained and modulus maxima points of different positions caused by noises are eliminated. The modulus maxima of each level are searched with the Adhoc algorithm step by step and the denoised signals are reconstructed by alternating projection algorithm. This improved algorithm realized adaptive selection of threshold values and removal of wrongly selected modulus maxima pickup points. Our method and a conventional denoising method were both applied to simulation signal processing, and comparative analysis verified effectiveness of our improved method.