Optimization-based simultaneous alignment and reconstruction in multi-element tomography.

As x-ray microscopy is pushed into the nanoscale with the advent of more bright and coherent x-ray sources, associated improvement in spatial resolution becomes highly vulnerable to geometrical errors and uncertainties during data collection. We address a form of error in tomography experiments, namely, the drift between projections during the tomographic scan. Our proposed method can simultaneously recover the drift, while tomographically reconstructing the specimen based on a joint iterative optimization scheme. This approach utilizes the correlation provided from different view angles and different signals. While generally applicable, we demonstrate our method on x-ray fluorescence tomography from a tissue specimen and compare the reconstruction quality with conventional methods.

Joint ptycho-tomography reconstruction through alternating direction method of multipliers.

We present the extension of ptychography for three-dimensional object reconstruction in a tomography setting. We describe the alternating direction method of multipliers (ADMM) as a generic reconstruction framework to efficiently solve the nonlinear optimization problem. In this framework, the ADMM breaks the joint reconstruction problem into two well-defined subproblems: ptychographic phase retrieval and tomographic reconstruction. In this paper, we use the gradient descent algorithm to solve both problems and demonstrate the efficiency of the proposed approach through numerical simulations. Further, we show that the proposed joint approach relaxes existing requirements for lateral probe overlap in conventional ptychography. Thus, it can allow more flexible data acquisition.

Joint reconstruction of x-ray fluorescence and transmission tomography.

X-ray fluorescence tomography is based on the detection of fluorescence x-ray photons produced following x-ray absorption while a specimen is rotated; it provides information on the 3D distribution of selected elements within a sample. One limitation in the quality of sample recovery is the separation of elemental signals due to the finite energy resolution of the detector. Another limitation is the effect of self-absorption, which can lead to inaccurate results with dense samples. To recover a higher quality elemental map, we combine x-ray fluorescence detection with a second data modality: conventional x-ray transmission tomography using absorption. By using these combined signals in a nonlinear optimization-based approach, we demonstrate the benefit of our algorithm on real experimental data and obtain an improved quantitative reconstruction of the spatial distribution of dominant elements in the sample. Compared with single-modality inversion based on x-ray fluorescence alone, this joint inversion approach reduces ill-posedness and should result in improved elemental quantification and better correction of self-absorption.

Non-negative matrix analysis for effective feature extraction in X-ray spectromicroscopy.

X-Ray absorption spectromicroscopy provides rich information on the chemical organization of materials down to the nanoscale. However, interpretation of this information in studies of "natural" materials such as biological or environmental science specimens can be complicated by the complex mixtures of spectroscopically complicated materials present. We describe here the shortcomings that sometimes arise in previously-employed approaches such as cluster analysis, and we present a new approach based on non-negative matrix approximation (NNMA) analysis with both sparseness and cluster-similarity regularizations. In a preliminary study of the large-scale biochemical organization of human spermatozoa, NNMA analysis delivers results that nicely show the major features of spermatozoa with no physically erroneous negative weightings or thicknesses in the calculated image.

Unsupervised cell identification on multidimensional X-ray fluorescence datasets.

A novel approach to locate, identify and refine positions and whole areas of cell structures based on elemental contents measured by X-ray fluorescence microscopy is introduced. It is shown that, by initializing with only a handful of prototypical cell regions, this approach can obtain consistent identification of whole cells, even when cells are overlapping, without training by explicit annotation. It is robust both to different measurements on the same sample and to different initializations. This effort provides a versatile framework to identify targeted cellular structures from datasets too complex for manual analysis, like most X-ray fluorescence microscopy data. Possible future extensions are also discussed.