Yield-Adjusted Operation for Convolution Filter Denoising

A perfect denoising for measurement shall remove noise, while keeping signal truth, so it is a dual-objective optimization of the signal yield and the noise residue. The frequency difference between the noise and signal is the basis of band-limited filter denoising. The root cause for the sharp peak denoise distortion is the insufficient spectrum sampling because of the scattered frequency distribution, which makes it hard to achieve dual-objective optimization. Thus, this article proposes a four-step operation of the signal yield adjustment for beyond the band-limited system. The first step is identifying the signal and noise levels in raw data, then adjusting the sampling density of high-signal level areas and enriching it by linear interpolation, then smoothing the reshaped profile, which is friendly to the filter, and finally, restoring the deformed one to its original form. An executable script function has fully achieved the whole operation. Some actual sharp spectra (Raman, NMR, laser-induced breakdown spectroscopy, and X-ray diffraction) make a comparison between the way with the Savitzky-Golay (SG) method and wavelet (multi-scale) denoising. The results show that all the effects are better than those of the SG filter, all estimations of the yield of signals are more than 99%, and the residue of noise is less than 10%. With multi-scale denoising, this operation is more targeted and gets more rational spectrum profiles─noise reduction without spectrum distortion.