Inversion of photon correlation spectroscopy based on truncated singular value decomposition and cascadic multigrid technology

Abstract

For the low accuracy of single-scale inversion method in photon correlation spectroscopy technology, a cascadic multigrid (CMG)-truncated singular value decomposition (TSVD) inversion method that combines the TSVD regularization with CMG technology is proposed. This method decomposes the original problem into several subproblems in different scale grid space. According to the particle sizes inverted from the coarsest scale to the finest scale, the solution of an original inversion problem can be obtained. For the inversion of each subproblem, TSVD method is used. The simulation and experimental data were respectively inverted by TSVD and CMG-TSVD methods. The inversion results demonstrate that the CMG-TSVD method has higher accuracy, more strong noise immunity and better smoothness than the TSVD method.

Research on the Spectral Reconstruction of a Low-Dimensional Filter Array Micro-Spectrometer Based on a Truncated Singular Value Decomposition-Convex Optimization Algorithm

“…Truncated singular value decomposition [19][20] is a classic method for dealing with large condition number matrices. After the matrix undergoes singular value decomposition, a set of Singular values matrices arranged from large to small are generated as shown in Eq.…”

Hypothesis Test of the Photon Count Distribution for Dust Discrimination in Dynamic Light Scattering

“…Therefore, DLS analysis through photon correlation spectroscopy (PCS) and autocorrelation functions have been in the focus for a long time . To analyze the correlation function, the method of cumulants − and CONTIN , are the most cited approaches, although many alternatives and improvements have been proposed. ,− These include Bayesian analysis, maximum entropy, and neural network models. − All these approaches address the intensity auto correlation function, while it is well-known that the analysis of the correlation function is an ill-posed inverse problem, which becomes unreliable as soon as there is dust in the sample. In such cases, the correlation function displays multiple decays, and by inspecting solely the correlation function, one cannot discriminate between intensity fluctuations from, e.g., dust and those from larger but otherwise regular NPs.…”