Scale Analysis of Wavelet Regularization Inversion and Its Improved Algorithm for Dynamic Light Scattering

In the large inversion range, the wavelet-regularization inversion method (WRIM) is an effective method for improving the inversion accuracy of dynamic light scattering (DLS) data. However, the initial decomposition scale (IDS) of this method has a great effect on the inversion accuracy. The particle size distribution (PSD) obtained from inappropriate IDS is not optimal. We analyze the effect of the different IDS on the inversion result in this paper. The results show that IDS of the smallest relative error should be chosen as the optimal IDS. However, because the true PSD is unknown in the practical measurements, this optimal IDS criterion is infeasible. Therefore, we propose an application criterion determining the optimal IDS. Based on this criterion, an improved WRIM with the optimal IDS is established. By the improved WRIM, high accuracy inversion PSD is obtained from DLS data. The simulated and experimental data demonstrate the effectiveness of this algorithm. Besides, we also further study the effect of the data noise on the optimal IDS. These studies indicate that the optimal IDS usually shows a downward trend with an increase of noise level.