Lp-norm-residual constrained regularization model for estimation of particle size distribution in dynamic light...

In particle size measurement using dynamic light scattering (DLS), noise makes the estimation of the particle size distribution (PSD) from the autocorrelation function data unreliable, and a regularization technique is usually required to estimate a reasonable PSD. In this paper, we propose an Lp-norm-residual constrained regularization model for the estimation of the PSD from DLS data based on the Lp norm of the fitting residual. Our model is a generalization of the existing, commonly used L2-norm-residual-based regularization methods such as CONTIN and constrained Tikhonov regularization. The estimation of PSDs by the proposed model, using different Lp norms of the fitting residual for p=1, 2, 10, and ∞, is studied and their performance is determined using simulated and experimental data. Results show that our proposed model with p=1 is less sensitive to noise and improves stability and accuracy in the estimation of PSDs for unimodal and bimodal systems. The model with p=1 is particularly applicable to the noisy or bimodal PSD cases.