In general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.

Electron tomography is a powerful tool in materials science to characterize nanostructures in three dimensions (3D). In scanning transmission electron microscopy (STEM), the sample under study is exposed to a focused electron beam and tilted to obtain twodimensional (2D) projections at different angles; many imaging modes are available such as high-angle annular dark-field (HAADF). In tomography, the collection of projections is called a tilt-series, from which we can reconstruct a 3D image that represents the sample. While HAADF tomography can clearly reveal the inner structure of the sample, it cannot directly provide compositional information. To better understand nanomaterials with more types of elements, spectral imaging techniques like energy dispersive X-ray spectroscopy (EDS) must be pursued. EDS tomography, however, is currently hampered by slow data acquisition, resulting in a small number of elemental maps with low signalto- noise ratio (SNR). Electron tomography, especially EDS tomography, is an ill-posed inverse problem whose solution is not stable and unique. Although advanced reconstruction techniques may yield a more accurate result by incorporating prior knowledge, they also involve fine-tuning parameters that highly influence the reconstruction quality. Furthermore, while great efforts have been dedicated to developing tomography techniques for image enhancement, directly combining reconstruction volumes at hand has still not been widely considered to the best of our knowledge.

In this paper, we present a multichannel cross-modal fusion algorithm to combine two complementary modalities in electron tomography: X-ray spectroscopy and scanning transmission electron microscopy (STEM). The former reveals compositions with high elemental specificity but low signal-to-noise ratio (SNR), while the latter characterizes the structure with high SNR but little chemical information. We use a multivariate regression to build a cross-modal fusion framework for these two modalities to simultaneously achieve high elemental specificity and high SNR for a target element chosen from the sample under study. Specifically, we first compute three-dimensional tomograms from tilt-series datasets of X-ray and STEM using different reconstruction algorithms. Then, we generate many feature images from each tomogram. Finally, we adopt partial least squares regression to assess the connection between these feature images and the reconstruction of the target element. Based on the simulated and experimental datasets of semiconductor devices, we demonstrate that our algorithm can not only produce continuous edges, homogeneous foreground, and clean background in its element-specific reconstructions but also can more accurately preserve fine structures than state-of-the-art tomography techniques. Moreover, we show that it can deliver results with high fidelity even for X-ray datasets with limited tilts or low counts. This property is highly desired in the semiconductor industry where acquisition time and sample damage are essential.

Regularization has been introduced to electron tomography for enhancing the reconstruction quality. Since over-regularization smears out sharp edges and under-regularization leaves the image too noisy, finding the optimal regularization strength is crucial. To this end, one can either manually tune regularization parameters by trial and error, or compute reconstructions for a large set of candidate values and compare them to a reference image. Both are cumbersome in practice. In this paper, we propose an image quality metric Q to quantify the reconstruction quality for automatically determining the optimal regularization parameter without a reference image. Specifically, we use the oriented structure strength described by the highest two responses in orientation space to simultaneously measure the sharpness and noisiness of reconstruction images. We demonstrate the usefulness of Q on a recently introduced total nuclear variation regularized reconstruction technique using simulated and experimental datasets of core-shell nanoparticles. Results show that it can replace the full-reference correlation coefficient to find the optimal. Moreover, observing that the curve of Q versus has a distinct maximum attained for the best quality, we adopt the golden section search for the optimum to effectively reduce the computational time by 85%.

Bimodal tomography introduces a weighting factor α to incorporate X-ray data into projection images acquired from scanning transmission electron microscope (STEM) for achieving an atom-specific three-dimensional (3D) reconstruction of an object on the nanoscale. Currently its value is chosen by computing reconstructions for a large range of αin(0,1) and comparing them to a hand-segmented ground truth with the mean square error (MSE). Since this is infeasible for an industrial application, in this paper we propose an image quality metric to quantify the quality of tomograms in terms of cross-atomic contamination and noise for selecting the weighting factor without a ground truth. Numerical results demonstrate that our framework can determine close-to-optimal weighting factor within an accuracy of pm 0.03. Moreover, approximating the shape of the minimum by a parabola effectively reduces the computational time by 90%.

With electron tomography, we can reconstruct a threedimensional
(3D) volume of a specimen from a series of its two-dimensional (2D) projection images on the nanoscale. In a scanning transmission electron microscope (STEM), element-specific maps and mass-contrast projections can be simultaneously acquired from the X-ray spectrometer and electron detector. The X-ray tomogram has high chemical specificity but low signal-to-noise ratio (SNR), while the electron tomogram has poor compositional information but high
SNR. In this paper, we adopt and modify a regression-based image fusion algorithm to combine these two complementary modalities, so that the fused version would maintain both high chemical specificity and high SNR. We demonstrate that our method improves reconstruction quality on an experimental dataset of a core-shell nanoparticle. Specifically, it delivers tomograms with sharper edges and smoother fore- and background, and hence can enable easier and more accurate 3Dcharacterization of such nanostructures.