A V-curve criterion for the parameter optimization of the Tikhonov regularization inversion algorithm for particle sizing

The regularization parameter plays an important role in applying the Tikhonov regularization method to recover the particle size distribution from dynamic light scattering experiments. The so-called V-curve, which is a plot of the product of the residual norm and the norm of the recovered distribution versus all valid regularization parameters, can be used to estimate the result of inversion. Numerical simulation demonstrated that the resultant V-curve can be applied to optimize the regularization parameter. The regularization parameter is optimized corresponding to the minimum value of the V-curve. Simulation and experimental results show that stable distributions can be retrieved using the Tikhonov regularization with optimum parameter for unimodal particle size distributions.

► The regularization parameter plays an important role in applying the Tikhonov regularization method. ► We use two criteria including residual error and the norm of recovered distribution to estimate the result of inversion. In order to overcome the shortcoming of these two criteria, the so-called V-curve criterion was used. ► Numerical simulation demonstrated that V-curve criterion can be applied to optimize the regularization parameter. ► Experimental results show that stable distributions can be retrieved using the Tikhonov method with optimum parameter.