Plug-and-play (PnP) methods have recently emerged as a powerful framework for image reconstruction that can flexibly combine different physics-based observation models with data-driven image priors in the form of denoisers, and achieve state-of-the-art image reconstruction quality in many applications. In this paper, we aim to further improve the computational efficacy of PnP methods by designing a new algorithm that makes use of stochastic variance-reduced gradients (SVRG), a nascent idea to accelerate runtime in stochastic optimization. Compared with existing PnP methods using batch gradients or stochastic gradients, the new algorithm, called PnP-SVRG, achieves comparable or better accuracy of image reconstruction at a much faster computational speed. Extensive numerical experiments are provided to demonstrate the benefits of the proposed algorithm through the application of compressive imaging using partial Fourier measurements in conjunction with a wide variety of popular image denoisers.

This paper explores the idea of modeling a large image data collection of polycrystal electron patterns, in order to detect insights in understanding materials discovery. There is an emerging interest in applying big data processing, management and modeling methods to scientific images, which often come in a form and with patterns only interpretable to domain experts. While large-scale machine learning approaches have demonstrated certain superiority in analyzing, summarizing, and providing an understandable route to data types like natural images, speeches and texts, scientific images is still a relatively unexplored area. Deep convolutional neural networks, despite their recent triumph in natural image understanding, are still rarely seen adapted to experimental microscopic images, especially in a large scale. To the best of our knowledge, we present the first deep learning solution towards a scientific image indexing problem using a collection of over 300K microscopic images. The result obtained is 54% better than a dictionary lookup method which is state-of-the-art in the materials science society.

X-ray tomography is increasingly being used for 4D spatio-temporal imaging of material samples at micron and finer scales. However, the temporal resolution of widely used 4D reconstruction methods is severely limited by the need to acquire a very large number of views for each reconstructed 3D volume. In this paper, we present a time interlaced model-based iterative reconstruction (TIMBIR) method which can significantly improve the temporal resolution of reconstructions. TIMBIR is a synergistic combination of two innovations. The first innovation, interlaced view sampling, is a novel approach to data acquisition which distributes the view angles more evenly in time. The second innovation is a 4D model based iterative reconstruction algorithm (MBIR) which can produce time resolved volumetric reconstructions of the sample from the interlaced views. Reconstructions of simulated data indicate that TIMBIR can improve the temporal resolution by an order of magnitude relative to existing approaches.

Enforcing a specific topology in image segmentation is a very important but challenging problem, which has attracted much attention in the computer vision community. Most recent works on topology-constrained image segmentation focus on binary segmentation, where the topology is often described by the connectivity of both foreground and background. In this paper, we develop a new multi-labeling method to enforce topology in multi-label image segmentation. In this case, we not only require each segment to be a connected region (intra-segment topology), but also require specific adjacency relations between each pair of segments (inter-segment topology). We develop our method in the context of segmentation propagation, where a segmented template image defines the topology, and our goal is to propagate the segmentation to a target image while preserving the topology. Our method requires good spatial structure continuity between the template and the target such that the template segmentation can be used as a good initialization for segmenting the target. In addition, we focus on multi-label segmentation where a segment and its adjacent segments form a ring structure, which is among the most complex type of inter-segment topology for 2D structures. We apply the proposed method to segment 3D metallic image volumes for the underlying grain structures and achieve better results than several comparison methods. Finally, we also apply the proposed method to interactive segmentation and stereo matching applications.

This letter considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of distributions over the sphere that are invariant to the actions of a finite spherical symmetry group G, a group-invariant extension of the Von Mises Fisher (VMF) distribution is obtained. The G-invariant VMF is parameterized by location and scale parameters that specify the distribution's mean orientation and its concentration about the mean, respectively. Using the restricted finite mixture representation these parameters can be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. This is illustrated for the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.

Markov random field (MRF) models have become extremely popular for regularization in image segmentation. They are useful for imposing local constraints, but they have limited capability for imposing global constraints. Marked Point Process (MPP) models incorporate global information, such as shape, as a prior, but local constraints, such as pixel-wise interaction, are not easily modeled. In this paper, we propose a combined MRF and MPP model and demonstrate its usefulness for micrograph analysis. Our hybrid model imposes both local and global constraints, at the pixel level as well as the object level. A multiple birth and death algorithm is then used to approximate the MAP segmentation using the hybrid model. We present experimental results to show the advantage of our model over the MPP for object identification and the MRF for segmentation.

We propose a segmentation and anomaly detection method for electron backscatter diffraction (EBSD) images. In contrast to conventional methods that require Euler angles to be extracted from diffraction patterns, the proposed method operates on the patterns directly. We use a forward model implemented as a dictionary of diffraction patterns generated by a detailed physics-based simulation of EBSD. The combination of full diffraction patterns and a dictionary allows anomalies to be detected at the same time as grains are segmented, and also increases robustness to noise and instrument blur. The proposed method is demonstrated on a sample of the Ni-base alloy IN100.

High angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) data is increasingly being used in the physical sciences to research materials in 3D because it reduces the effects of Bragg diffraction seen in bright field TEM data. Typically, tomographic reconstructions are performed by directly applying either filtered back projection (FBP) or the simultaneous iterative reconstruction technique (SIRT) to the data. Since HAADF-STEM tomography is a limited angle tomography modality with low signal to noise ratio, these methods can result in significant artifacts in the reconstructed volume. In this paper, we develop a model based iterative reconstruction algorithm for HAADF-STEM tomography. We combine a model for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a maximum a posteriori probability (MAP) estimation problem. Our formulation also accounts for certain missing measurements by treating them as nuisance parameters in the MAP estimation framework. We adapt the iterative coordinate descent algorithm to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

Segmentation propagation, similar to tracking, is the problem of transferring a segmentation of an image to a neighboring image in a sequence. This problem is of particular importance to materials science, where the accurate segmentation of a series of 2D serial-sectioned images of multiple, contiguous 3D structures has important applications. Such structures may have distinct shape, appearance, and topology, which can be considered to improve segmentation accuracy. For example, some materials images may have structures with a specific shape or appearance in each serial section slice, which only changes minimally from slice to slice, and some materials may exhibit specific inter-structure topology that constrains their neighboring relations. Some of these properties have been individually incorporated to segment specific materials images in prior work. In this paper, we develop a propagation framework for materials image segmentation where each propagation is formulated as an optimal labeling problem that can be efficiently solved using the graph-cut algorithm. Our framework makes three key contributions: 1) a homomorphic propagation approach, which considers the consistency of region adjacency in the propagation; 2) incorporation of shape and appearance consistency in the propagation; and 3) a local non-homomorphism strategy to handle newly appearing and disappearing substructures during this propagation. To show the effectiveness of our framework, we conduct experiments on various 3D materials images, and compare the performance against several existing image segmentation methods.