Inversion model for extracting chemically resolved depth profiles across liquid interfaces of various configurations from XPS data: PROPHESY

PROPHESY, a technique for the reconstruction of surface-depth profiles from X-ray photoelectron spectroscopy data, is introduced. The inversion methodology is based on a Bayesian framework and primal-dual convex optimization. The acquisition model is developed for several geometries representing different sample types: plane (bulk sample), cylinder (liquid microjet) and sphere (droplet). The methodology is tested and characterized with respect to simulated data as a proof of concept. Possible limitations of the method due to uncertainty in the attenuation length of the photo-emitted electron are illustrated.

Quantitative alignment parameter estimation for analyzing X-ray photoelectron spectra

The interpretation of X-ray photoelectron spectroscopy (XPS) data relies on measurement models that depend on several parameters, including the photoelectron attenuation length and X-ray photon flux. However, some of these parameters are not known, because they are not or cannot be measured. The unknown geometrical parameters can be lumped together in a multiplicative factor, the alignment parameter. This parameter characterizes the ability of the exciting light to interact with the sample. Unfortunately, the absolute value of the alignment parameter cannot be measured directly, in part because it depends on the measurement model. Instead, a proxy for the experimental alignment is often estimated, which is closely related to the alignment parameter. Here, a method for estimating the absolute value of the alignment parameter based on the raw XPS spectra (i.e. non-processed photoelectron counts), the geometry of the sample and the photoelectron attenuation length is presented. The proposed parameter estimation method enables the quantitative analysis of XPS spectra using a simplified measurement model. All computations can be executed within the open and free Julia language framework PROPHESY. To demonstrate feasibility, the alignment parameter estimation method is first tested on simulated data with known acquisition parameters. The method is then applied to experimental XPS data and a strong correlation between the estimated alignment parameter and the typically used alignment proxy is shown.

Global Diffusion Tractography by Simulated Annealing

OBJECTIVE

Our goal is to develop a robust global tractography method for cardiac diffusion imaging.

METHODS

A graph is stretched over the whole myocardium to represent the fiber structure, and the solutions are minima of a graph energy measuring the fidelity to the data along with the fiber density and curvature. The optimization is performed by a variant of simulated annealing that offers increased design freedom without sacrificing theoretical convergence guarantees.

RESULTS

Numerical experiments on synthetic and real data demonstrate the capability of our tractography algorithm to deal with low angular resolution, highly noisy data. In particular, our algorithm outperforms the Bayesian model-based algorithm of Reisert et al. (NeuroImage, vol. 54, no. 2, 2011) and the graph-based algorithm of Frindel et al. (Magn. Reson. Med., vol. 64, no. 4, 2010) at the noise levels typical of in vivo imaging.

CONCLUSION

The proposed algorithm avoids the drawbacks of local techniques and is very robust to noise, which makes it a promising tool for in vivo diffusion imaging of moving organs.

SIGNIFICANCE

Our approach is global in terms of both the fiber structure representation and the minimization problem. It also allows us to adjust the trajectory density by simply changing the vertex-lattice spacing in the graph model, a desirable feature for multiresolution tractography analysis.