Inversion PCS Particle Size Distribution Based On The Total Variation Regularization Method

The particle size inversion in PCS particle measurement technology has been an important and attractive research topic. Regularization method as a widely used method, its performance depends on the regularization parameter and the regularization operator. The determination of appropriate regularization parameter and the construction of regularization operator are two core issues to regularization method. On regularization parameter selection, there are a lot of more mature theories, such as the L-curve criterion, generalized cross-validation criterion and proposed optimal criterion. In particle size distribution inversion, more people study the Tikhonov regularization method which used linear regularization operator. This paper analyzed total variation regularization theory with nonlinear regularization operator, studied its application conditions, the difference of results compared to the Tikhonov regularization and efficiency of the algorithm.The main work of this paper consists of:1. The characteristics of total variation regularization were studied and several methods solving the total variation regularization problem were analyzed, the steepest descent method, Newton's method and lagged diffusivity fixed point iteration. Steepest descent method is simple, reliable, and linear convergence, but the search step size selected is no definite method; Newton's method quadratic convergence, but also need to determine in advance the search step. We used lagged diffusivity fixed point iteration method to solve the total variation regularization problem and proved it's globally convergent.2. The relationship between the smooth factor in the total variation regularization operator and distribution error were analyzed, and according to this relationship, we determined the optimal smooth factor. The smooth factor value how to impact the anti-noise performance of the algorithm was studied.3. The retrieval accuracy between total variation method and Tikhonov method were compared. The total variation regularization method was used to inverse simulation distribution of177nm narrow single peak,572nm wide single peak,215nm single peak,84and241nm,210and716nm bimodal distribution, its peak ratios were2.83:1and3.4:1respectively. The results obtained by non-negative total variation regularization method were compared with results obtained by non-negative Tikhonov regularization method, and the algorithm performance and efficiency were evaluated.4. The performance of the algorithm was verified by inversion of measured mono-dispersed and polydispersity data. We proposed total variation regularization inversion of the measured60nm,150nm,200nm,300nm,450nm mono-dispersed data,60and200nm,150and300nm,200and450nm polydispersity data. The conclusions obtained from the experimental data with the consistency of the conclusions obtained by the simulation data were verified. Regularization method as one of the main method for inversion of particle size distribution in PCS technology, this paper analyzed the total variation regularization method with nonlinear regularization operator. This method has advantages in the inversion accuracy, the performance of anti-noise and this study contributed to the development of the PCS particle measurement technology.