Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic...

Area of Science:

• * Applied Mathematics
• * Physical Chemistry
• * Materials Science

Background:

• * Dynamic Light Scattering (DLS) is a crucial technique for determining particle size distribution.
• * Solving the inverse problem in DLS often requires sophisticated algorithms to handle ill-posedness.
• * Existing methods like CONTIN have limitations in certain scenarios.

Purpose of the Study:

• * To develop a novel nonnegative least-squares truncated singular value decomposition (NNLS-TSVD) method for DLS data analysis.
• * To establish and utilize a weak symmetry relationship between relative error and solution norm for parameter optimization.
• * To provide a powerful and simple alternative for solving the inverse problem in DLS.

Main Methods:

• * Development of a NNLS-TSVD algorithm incorporating a weak symmetry relationship.
• * Optimization of regularization parameters based on the identified error-norm relationship.
• * Application of the algorithm to recover particle size distribution from simulated and experimental DLS data.

Main Results:

• * The developed NNLS-TSVD method demonstrated a valid weak symmetry relationship.
• * Optimal regularization parameters were effectively specified using this relationship.
• * Simulated and experimental results confirmed the method's capability in recovering particle size distributions.

Conclusions:

• * The proposed NNLS-TSVD method offers a powerful and simple approach to the DLS inverse problem.
• * It complements existing algorithms such as CONTIN, providing an alternative for particle size analysis.
• * The method's effectiveness is validated through both simulated data and real-world experimental measurements.