Singular value analysis and reconstruction of photon correlation data equidistant in time

Abstract

The application of the algorithm of Zeiger and McEwen to the analysis of noisy photon correlation data is investigated. For the particular case where the data are sampled at equidistant time intervals a complete solution is given allowing reliable reconstruction of the spectrum of exponential decay rates without any a priori knowledge. A particular attractive feature of the method is that the singular value analysis of the Hankel matrix of autocorrelation functions offers a practical criterion for the decomposition of the data into a signal and a noise part. Some tests of the method are illustrated with experiments on monodisperse latices, gold sols, and binary mixtures of monodisperse latices. In the latter case comparable and even better results are obtained in significantly shorter computing time when compared to an analysis with Contin and the maximum entropy method. Since the present method does not require any a priori parameter setting, it is also complementary to these methods.

Dynamic light scattering: a practical guide and applications in biomedical sciences

“…Other methods including singular value and reconstruction methods were also developed, however, they are not as popular for the data analysis (Finsy et al 1989(Finsy et al , 1992. Koppel (1972) derived the cumulativegenerating function K(−τ, Γ) that is related to the logarithm of g 1 (τ) and the m th cumulant of distribution function k m (Γ):…”

Size Distributions out of Static Light Scattering: Inclusion of Distortions from the Experimental Setup, e.g., a SOFICA-type Goniometer

“…h͑a͒Ĩ͑, a͒da, [12] in which h(a) is the normalized number density of particles in [a, a ϩ da]. The distribution h(a) is the so-called sphere-size distribution (SSD).…”

“…Its solution has been tackled with several methods like the method of cumulants (10), maximum entropy analysis (11,14), singular value analysis (12), and Tikhonov regularization (13,17,27). The method of cumulants (10) and the singular value analysis (12) can only be applied to data which is described in terms of exponential functions; thus they are not applicable to SLS data.…”

Investigation of albumin-fullerenol interaction using laser correlation spectroscopy: the algorithm

“…The methods of regularisation and the entropy maximum allow the results close in accuracy, the regularisation methods operating almost twice as fast as the entropy maximum method [9]. At the same time, none of these methods yields "non-blurred" distributions in the case when many closely spaces peaks are present in the solution.…”

“…As a base, we took the regularisation methods that possess greater stability against the errors and potentially can provide more information than the entropy maximum method [9].…”