Analysis of Non-negative Tikhonov and Truncated Singular Value Decomposition Regularization Inversion in Pcs

Considering non-negative characteristic of the particle size distribution (PSD), based on trust-regionreflective Newton method, two non-negative regularization methods of truncated singular value decomposition (TSVD) and Tikhonov (TIK) for photon correlation spectroscopy (PCS) are proposed in this paper. Combining two regularization parameter criterions of GCV and L-curve, two non-negative regularization methods are studied. The study results show that, compared with TIK, TSVD has bigger truncation effect, poorer smoothness and narrower distribution width of inversion PSD, in the case of noise, TSVD has smaller relative error and peak value error of PSD, better capacity to discriminate bimodality and stronger anti-noise, but at noise-free case, TSVD hasn’t obvious advantages, TIK and TSVD are respectively more suitable for using GCV and L-curve criterion to determine the regularization parameter.