Sparse Bayesian learning for the Laplace transform inversion in dynamic light scattering

Characterisation of particles in solution – a perspective on light scattering and comparative technologies

“…This can be overcome by using the SBL analysis modes to generate size distributions for the sample [28]. Here, the size distribution is calculated based on the residues (quality of fit) ( x -axis) and sparsity index (size of the regularised solution ( Ng )) ( y -axis) of the L curve [28], with the most probable PSD having the lowest sparsity and residue index. Briefly, this L curve is a visualisation of the trade-off between the complexity of the fitting, i.e.…”

“…The optimal Ng lies at the vertex of the L curve. True distribution in the data can be difficult to obtain in this manner; however, as noise in the data can limit the detection of components of the system [28]. The work by Nyeo and Ansari [28] demonstrates the use of SBL to reconstruct bimodal distributions from DLS data, as shown in Figure 6.…”

“…True distribution in the data can be difficult to obtain in this manner; however, as noise in the data can limit the detection of components of the system [28]. The work by Nyeo and Ansari [28] demonstrates the use of SBL to reconstruct bimodal distributions from DLS data, as shown in Figure 6. Here, the authors use SBL to reconstruct the PSDs of crystalline protein from the ocular lens using experimental DLS data.

10.1080/14686996.2018.1517587-F0006Figure 6.The use of Sparse Bayesian Learning (SBL) to reconstruct bimodal size distributions from DLS data (a).

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“…A value of Ng = 18 yields the most probable particle size distribution (PSD), as it is the lowest value on both x - and y -axis (b). Reused with permission from Nyeo and Ansari [28]. …”

Spectral sparse Bayesian learning reflectivity inversion

“…The SBL model is known to enjoy many advantages, such as probabilistic prediction, the facility to utilize arbitrary basis functions and automatic estimation of nuisance parameters. This model has been successful in a wide range of applications such as visual tracking (Williams, Blake and Cipolla 2005), text classification (Silva and Ribeiro 2006), image processing (Demir and Erturk 2007), positron emission tomography (Peng et al 2008) and dynamic light scattering (Nyeo and Ansari 2011).…”