Singular value decomposition as a tool for background corrections in time-resolved XFEL scattering data

Abstract

The development of new X-ray light sources, XFELs, with unprecedented time and brilliance characteristics has led to the availability of very large datasets with high time resolution and superior signal strength. The chaotic nature of the emission processes in such sources as well as entirely novel detector demands has also led to significant challenges in terms of data analysis. This paper describes a heuristic approach to datasets where spurious background contributions of a magnitude similar to (or larger) than the signal of interest prevents conventional analysis approaches. The method relies on singularvalue decomposition of no-signal subsets of acquired datasets in combination with model inputs and appears generally applicable to time-resolved X-ray diffuse scattering experiments.

Methods for analysis of size-exclusion chromatography–small-angle X-ray scattering and reconstruction of protein scattering

“…SVD has been widely used to identify the number of unique components in data sets that can be represented in matrix form, including SAXS and SEC-SAXS (Haldrup, 2014;Sadygov, 2014;Man et al, 2014;Fetler et al, 1995;Pé rez & Nishino, 2012;Gunn et al, 2011;David & Pé rez, 2009;Watanabe & Inoko, 2009;Pé rez et al, 2001;Lambright et al, 1991). In the present application, SVD is applied directly to the normalized data sets without buffer subtraction and used initially to identify a contiguous or even non-contiguous range of data sets with only two significant components corresponding to buffer and protein scattering.…”

“…Thus, objective assessment of data quality, and in particular the number of significant species, is essential for analysis of mixtures by SEC-SAXS. Singular value decomposition (SVD) has been used to diagnose uniqueness and increase signal-to-noise in complex biophysical and biochemical data sets (Haldrup, 2014;Sadygov, 2014;Man et al, 2014;Pé rez et al, 2001;Fetler et al, 1995;Lambright et al, 1991), and has found a number of uses for analysis of SAXS data (Kathuria et al, 2014;Brookes et al, 2013;Williamson et al, 2008;Pé rez et al, 2001;Fetler et al, 1995). SVD is a matrix algebra method that is particularly useful for determining the minimum number of components required to accurately represent data sets with a high redundancy.…”

The birth of a new field

“…The machine, in a 2-mile-long tunnel near Stanford, generates 120 pulses of hard or soft X-rays per second, containing about 1 Â 10 12 photons per 10 fs pulse, and, using purpose-built detectors, allows the diffraction pattern from each pulse to be read-out and saved. Broadly, three types of experiments were first attempted-those in which hydrated protein nanocrystals were sprayed across the pulsed beam (serial femtosecond nanocrystallography, SFX), those in which the hard X-ray beam of micrometre dimensions traverses many biomolecules in a liquid jet (fast solution scattering, FSS-see contributions by Haldrup [4], Mendez et al [5] and Pande et al [6]), and single particle (SP) imaging, in which a beam of submicrometre dimensions scatters from an SP such as a virus [7][8][9]. Before long many other experimental arrangements had also been tried during this exciting first 4 years, including fixed samples scanned across the beam for the study of two-dimensional membrane protein crystals [10], time-resolved SFX [11] (see also Moffat [12]), and new types of sample delivery devices, such as those based on the lipid cubic phase [13,14] and on electrospraying [15].…”

Ultra-high resolution and broadband chip-scale speckle enhanced Fourier-transform spectrometer

“…Figure 3 (e) is the comparison of singular values for various devices at a wider bandwidth regime (10 nm with 0.01 nm steps). A large number of distinctive eigenfunctions with larger values allows for better signal reconstruction [15,24,25]. The SDFT spectrometer consists of 64 large singular values corresponding to the 64 MZI channels that provide coarse resolution and additional ∼ 500 smaller eigenvalues corresponding to highfrequency eigenfunctions that provides enhancement in spectral resolution.…”