Inversion Of Particle Size Distribution From Light Scattering Data With Iterative Regularization Algorithms

The inversion of particle size distribution from measured (noisy) data of light scattering, as a typical inverse problem, has been studied by many reseachers and solved by several numerical methods. Among which, direct Tikhonov regularization method with Morozov discrepancy principle, is often used to overcome the ill-posedness linked with the Fredholm integral equation of the first kind, so the stability of inversion has been heightened. But there has much room for improvement of the inversion accuaracy, especially for the double-peak problems. As a new attempt, this paper is devoted to this end by employing iterated Tikhonov regulariztion and Pade iterative regularition. The related algorithms are discriped, the convergence and error analysis are also given. The special emphasis is to present an improved version of well-known Morozov discrepancy principle with successful applications to iterated Tikhonov regularization. The theoretical analysis and tested results show that the proposed algorithms in this paper have a good stability and effectiveness.