Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and unstructured geometries, non-linearity of the data fitting and regularization terms, and non-differentiability of the regularization term. We develop several approaches to overcome these difficulties by: i) defining discrete differential operators for unstructured geometries using both finite element and graph representations; ii) developing an optimization algorithm based on the alternating direction method of multipliers (ADMM) for the non-differentiable and non-linear minimization problem; iii) investigating isotropic and anisotropic variants of TV regularization, and comparing their finite element- and graph-based implementations. These approaches are evaluated on experiments on simulated data and real data acquired from a tissue phantom. Our results show that both FEM and graph-based TV regularization is able to accurately reconstruct both sparse and non-sparse distributions without the over-smoothing effect of Tikhonov regularization and the over-sparsifying effect of L$_1$ regularization. The graph representation was found to out-perform the FEM method for low-resolution meshes, and the FEM method was found to be more accurate for high-resolution meshes.Comment: 24 pages, 11 figures. Reviced version includes revised figures and improved clarit

The use of random projections for the analysis of mass spectrometry imaging data

The ‘curse of dimensionality’ imposes fundamental limits on the analysis of the large, information rich datasets that are produced by mass spectrometry imaging. Additionally, such datasets are often too large to be analyzed as a whole and so dimensionality reduction is required before further analysis can be performed. We investigate the use of simple random projections for the dimensionality reduction of mass spectrometry imaging data and examine how they enable efficient and fast segmentation using k-means clustering. The method is computationally efficient and can be implemented such that only one spectrum is needed in memory at any time. We use this technique to reveal histologically significant regions within MALDI images of diseased human liver. Segmentation results achieved following a reduction in the dimensionality of the data by more than 99% (without peak picking) showed that histologic changes due to disease can be automatically visualized from molecular images. [Figure: see text] ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s13361-014-1024-7) contains supplementary material, which is available to authorized users

Comprehensive LESA Mass Spectrometry Imaging of Intact Proteins by Integration of Cylindrical FAIMS

The benefits of high field asymmetric waveform ion mobility spectrometry (FAIMS) for mass spectrometry imaging of intact proteins in thin tissue sections have been demonstrated previously. In those works, a planar FAIMS device coupled with a Thermo Elite mass spectrometer was employed. Here, we have evaluated a newly introduced cylindrical FAIMS device (the FAIMS Pro) coupled with a Thermo Fusion Lumos mass spectrometer for liquid extraction surface analysis mass spectrometry imaging of intact proteins in thin tissue sections from rat testes, kidney, and brain. The method makes use of multiple FAIMS compensation values at each location (pixel) of the imaging array. A total of 975 nonredundant protein species were detected in the testes imaging dataset, 981 in the kidney dataset, and 249 in the brain dataset. These numbers represent a 7-fold (brain) and over 10-fold (testes, kidney) improvement on the numbers of proteins previously detected in LESA FAIMS imaging, and a 10-fold to over 20-fold improvement on the numbers detected without FAIMS on this higher performance mass spectrometer, approaching the same order of magnitude as those obtained in top-down proteomics of cell lines. Nevertheless, high throughput identification within the LESA FAIMS imaging workflow remains a challenge