The reconstruction of particle size distributions from dynamic light scattering data using particle swarm optimization techniques with different objective functions

Particle Size Inversion Constrained by L∞ Norm for Dynamic Light Scattering

“…If the data is noisy, the solution x may have large random fluctuations and present instability. The Tikhonov regularization method can effectively solve such ill-posed problems [ 9 ]. In the classical Tikhonov method, the L 2 norm regularization term is introduced into Equation (9) to constrain.…”

“…In practice, the existence of noise and rounding errors in ACF data may prevent the existence of solutions, or mean that the solutions are unstable or not unique. A variety of estimation methods have been proposed to accurately estimate PSD from DLS measurement data, including Tikhonov regularization [ 5 ], the accumulation method [ 8 ], the double exponential method [ 9 ], the exponential sampling method [ 10 ], the non-negative constrained least squares [ 11 ], the CONTIN algorithm [ 12 ], and others. Among these algorithms, Tikhonov regularization and the CONTIN based on imposing a regularization constraint on the data fitting terms are the most effective in estimating PSD [ 5 , 9 , 10 ].…”

“…A variety of estimation methods have been proposed to accurately estimate PSD from DLS measurement data, including Tikhonov regularization [ 5 ], the accumulation method [ 8 ], the double exponential method [ 9 ], the exponential sampling method [ 10 ], the non-negative constrained least squares [ 11 ], the CONTIN algorithm [ 12 ], and others. Among these algorithms, Tikhonov regularization and the CONTIN based on imposing a regularization constraint on the data fitting terms are the most effective in estimating PSD [ 5 , 9 , 10 ]. These algorithms use the solutions of a family of well-posed problems that are “adjacent” to the original ill-posed one to approximate the solution of the original problem and produce reasonable results [ 10 ].…”

Scale Analysis of Wavelet Regularization Inversion and Its Improved Algorithm for Dynamic Light Scattering

“…The small disturbances in the measurement data may lead to serious deviation in PSD. In order to deal with this problem, the numerous inversion approaches have been proposed to estimate the PSD from DLS data, such as the cumulants method [7,8], constrained regularization method (CONTIN) [9,10], Laplace transform method [11], the nonnegative leastsquares method (NNLS) [12], maximum likelihood method [13], exponential sampling method [14], nonnegative TSVD method [15], Bayesian inversion method [16][17][18], the maximum entropy method [19], and the various intelligences methods [20][21][22][23][24][25]. In addition, various improved algorithms have constantly emerged [26][27][28][29].…”