Penalized-Likelihood PET Image Reconstruction Using Similarity-Driven Median Regularization

In this paper, we present a new regularized image reconstruction method for positron emission tomography (PET), where an adaptive weighted median regularizer is used in the context of a penalized-likelihood framework. The motivation of our work is to overcome the limitation of the conventional median regularizer, which has proven useful for tomographic reconstruction but suffers from the negative effect of removing fine details in the underlying image when the edges occupy less than half of the window elements. The crux of our method is inspired by the well-known non-local means denoising approach, which exploits the measure of similarity between the image patches for weighted smoothing. However, our method is different from the non-local means denoising approach in that the similarity measure between the patches is used for the median weights rather than for the smoothing weights. As the median weights, in this case, are spatially variant, they provide adaptive median regularization achieving high-quality reconstructions. The experimental results indicate that our similarity-driven median regularization method not only improves the reconstruction accuracy, but also has great potential for super-resolution reconstruction for PET.

Three-dimensional tomographically reconstructed optical emission profiles of Hall thruster plasmas

A diagnostic system was developed for spectrally resolved, three-dimensional tomographic reconstruction of Hall thruster plasmas, and local intensity profiles of Xe I and Xe II emissions were reconstructed. In this diagnostic system, 28 virtual cameras were generated using a single, fixed charge-coupled device (CCD) camera by rotating the Hall thruster to form a sufficient number of lines of sight. The Phillips-Tikhonov regularization algorithm was used to reconstruct local emission profiles from the line-integrated emission signals. The reconstruction performance was evaluated using both azimuthally symmetric and asymmetric synthetic phantom images including 5% Gaussian white noise, which resulted in a root-mean-square error of the reconstruction within an order of 10-3 even for a 1% difference in the azimuthal intensity distribution. Using the developed system, three-dimensional local profiles of Xe II emission (541.9 nm) from radiative decay of the excited state 5p4(3P2)6p2[3]˚5/2 and Xe I emission (881.9 nm) from 5p5(2P˚3/2)6p2[5/2]3 were obtained, and two different shapes were found depending on the wavelength and the distance from the thruster exit plane. In particular, a stretched central jet structure was distinctively observed in the Xe II emission profile beyond 10 mm from the thruster exit, while gradual broadening was found in the Xe I emission. Approximately 10% azimuthal nonuniformities were observed in the local Xe I and Xe II intensity profiles in the near-plume region (< 10 mm), which could not be quantitatively distinguished by analysis of the frontal photographic image. Three-dimensional Xe I and Xe II intensity profiles were also obtained in the plume region, and the differences in the structures of both emissions were visually confirmed.

Inward diffusion driven by low frequency fluctuations in self-organizing magnetospheric plasma

The new findings for dynamic process of inward diffusion in the magnetospheric plasma are reported on the RT-1 experiment: (i) The evolution of local density profile in the self-organized process has been analysed by the newly developed tomographic reconstruction applying a deep learning method. (ii) The impact of neutral-gas injection excites low-frequency fluctuations, which continues until the peaked density profile recovers. The fluctuations have magnetic components (suggesting the high-beta effect) which have two different frequencies and propagation directions. The phase velocities are of the order of magnetization drifts, and both the velocities and the intensities increase in proportion to the electron density. The self-regulating mechanism of density profile works most apparently in the naturally made confinement system, magnetosphere, which teaches the basic physics of long-lived structures underlying every stationary confinement scheme.

New transform to project axisymmetric deflection fields along arbitrary rays

Axisymmetric tomography is used to extract quantitative information from line-of-sight measurements of gas flow and combustion fields. For instance, background oriented schlieren (BOS) measurements are typically inverted by tomographic reconstruction to estimate the density field of a high-speed or high-temperature flow. Conventional reconstruction algorithms are based on the inverse Abel transform, which assumes that rays are parallel throughout the target object. However, camera rays are not parallel, and this discrepancy can result in significant errors in many practical imaging scenarios. We present a generalization of the Abel transform for use in tomographic reconstruction of light-ray deflections through an axisymmetric target. The new transform models the exact path of camera rays instead of assuming parallel paths, thereby improving the accuracy of estimates. We demonstrate our approach with a simulated BOS scenario in which we reconstruct noisy synthetic deflection data across a range of camera positions. Results are compared to state-of-the-art Abel-based algorithms. Reconstructions computed using the new transform are consistently more stable and accurate than conventional reconstructions.

CURT1A and CURT1C mediate distinct stages of plastid conversion in Arabidopsis

The crystalline structure of prolamellar bodies (PLBs) and light-induced etioplasts-to-chloroplasts transformation have been investigated with electron microscopy methods. However, these studies suffer from chemical fixation artifacts and limited volumes of tomographic reconstruction. We have examined Arabidopsis thaliana cotyledon samples preserved by high-pressure freezing with scanning transmission electron tomography to visualize larger volumes in etioplasts and their conversion into chloroplasts. PLB tubules were arranged in a zinc blende-type lattice like carbon atoms in diamonds. Within 2 hours after illumination, the lattice collapsed from the PLB exterior and the disorganized tubules merged to form fenestrated sheets that eventually matured into lamellar thylakoids. These planar thylakoids emerging from PLBs overlapped or folded into grana stacks in PLBs’ vicinity. Since the nascent lamellae had curved membrane at their tips, we examined the localization of CURT1 proteins. CURT1A transcript was most abundant in de-etiolating cotyledon samples, and CURT1A concentrated at the peripheral PLB. In curt1a mutant etioplasts, thylakoid sheets were swollen and failed to develop stacks. In curt1c mutant, however, PLBs had cracks in their lattices, indicating that CURT1C contributes to cubic crystal growth under darkness. Our data provide evidence that CURT1A and CURT1C play distinct roles in the etioplast and chloroplast biogenesis.

A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling

A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements, for which angular information is sparse but the temporal information is rich. 3D attenuation maps are recovered by propagating an initial discretized density volume in time according to the advection equations using the Finite Volumes method with a total variation diminishing monotonic upstream-centered scheme (TVDMUSCL). The benefits and limitations of the algorithm are explored using dynamic granular system phantoms modelled via discrete elements and projected by an analytical ray model independent from the numerical ray model used in the reconstruction scheme. Three phantom scenarios of increasing complexity are presented and it is found that projections from only a few (unknowns:equations > 10) angles can be sufficient for characterisation of the 3D attenuation field evolution in time. It is shown that the artificial velocity field produced by the algorithm sub-iteration, which is used to propagate the attenuation field, can to some extent approximate the true kinematics of the system. Furthermore, it is found that the selection of a temporal interpolation scheme for projection data can have a significant impact on error build up in the reconstructed attenuation field.

Transmission Electron Microscopy Tilt-Series Data from In-Situ Chondrocyte Primary Cilia

The primary cilium has recently become the focus of intensive investigations into understanding the physical structure and processes of eukaryotic cells. This paper describes two tilt-series image datasets, acquired by transmission electron microscopy, of in situ chick-embryo sternal-cartilage primary cilia. These data have been released under an open-access licence, and are well suited to tomographic reconstruction and modelling of the cilium.

Novel U-net based deep neural networks for transmission tomography

BACKGROUND: The fusion of computer tomography and deep learning is an effective way of achieving improved image quality and artifact reduction in reconstructed images. OBJECTIVE: In this paper, we present two novel neural network architectures for tomographic reconstruction with reduced effects of beam hardening and electrical noise. METHODS: In the case of the proposed novel architectures, the image reconstruction step is located inside the neural networks, which allows the network to be trained by taking the mathematical model of the projections into account. This strong connection enables us to enhance the projection data and the reconstructed image together. We tested the two proposed models against three other methods on two datasets. The datasets contain physically correct simulated data, and they show strong signs of beam hardening and electrical noise. We also performed a numerical evaluation of the neural networks on the reconstructed images according to three error measurements and provided a scoring system of the methods derived from the three measures. RESULTS: The results showed the superiority of the novel architecture called TomoNet2. TomoNet2 improved the quality of the images according to the average Structural Similarity Index from 0.9372 to 0.9977 and 0.9519 to 0.9886 on the two data sets, when compared to the FBP method. This network also yielded the best results for 79.2 and 53.0 percent for the two datasets according to Peak-Signal-to-Noise-Ratio compared to the other improvement techniques. CONCLUSIONS: Our experimental results showed that the reconstruction step used in skip connections in deep neural networks improves the quality of the reconstructions. We are confident that our proposed method can be effectively applied to other datasets for tomographic purposes.