Random interpolation average for signal denoising

In order to suppress the pseudo-Gibbs phenomena in the thresholding denoising method and to improve denoising capability, a novel denoising method called the random interpolation average (RIA) scheme is proposed. The noisy signals are interpolated randomly so that the matching condition between the features of the noisy signal and that of the wavelet basis is changed. Then the thresholding denoising is applied to this interpolated signal to obtain the denoised signal. Thus, by each time interpolation and denoising, the authors will obtain an independent denoised signal. Finally, the pseudo-Gibbs phenomena will be suppressed by averaging all of the independent denoised signals. According to comparison of the signal-to-noise ratio (SNR) of four typical denoised signals, the threshold, shrinkage function, wavelet bases and interpolation scheme of the RIA scheme are optimised. The denoising capabilities of the thresholding denoising method, the translation-invariant scheme, the WienerChop algorithm and the RIA scheme are compared by simulations. The results indicate that the pseudo-Gibbs phenomena can be suppressed efficiently by the RIA scheme with universal threshold, firm shrinkage function, Coiflet families and third-order Lagrange interpolation. Compared to the other three methods, the SNR of the denoised signals in the RIA scheme is increased by 3.53, 0.7 and 1.4 dB, respectively. Both the smoothness and similarity of the signals are also improved by the RIA scheme.