Selection of Optimal Decomposition Layer for Thresholding Denoising Using Singular Spectrum Analysis and Wavelet Entropy

To optimize the number of decomposition layers in wavelet threshold denoising for ultrasonic signals, we propose a self-adaptive algorithm of determining the number of decomposition layers based on singular spectrum analysis and wavelet entropy. First the noise-containing signals are decomposed by discrete wavelet transform. The slope of the singular value spectrum for each layer is estimated. Then the wavelet entropy over the signal subinterval is calculated for each layer. Finally the optimal number of decomposition layer is determined by combining the entropy ratio of detail coefficients to original signal and the slope of the singular value spectrum. The performance of the algorithm is evaluated using signal-to-noise ratio (SNR) and the relative error of the peak value (REPV). Experiment shows that the algorithm can self-adaptively determine the optimal number of decomposition layers and filter out the noise contained in the ultrasonic signals. It not only increases the SNR, but also preserves valuable components of the original signal.