Stretched sinograms for limited-angle tomographic reconstruction with neural networks

We present a direct method for limited angle tomographic reconstruction using convolutional networks. The key to our method is to first stretch every tilt view in the direction perpendicular to the tilt axis by the secant of the tilt angle. These stretched views are then fed into a 2-D U-Net which directly outputs the 3-D reconstruction. We train our networks by minimizing the mean squared error between the network's generated reconstruction and a ground truth 3-D volume. To demonstrate and evaluate our method, we synthesize tilt views from a 3-D image of fly brain tissue acquired with Focused Ion Beam Scanning Electron Microscopy. We compare our method to using a U-Net to directly reconstruct the unstretched tilt views and show that this simple stretching procedure leads to significantly better reconstructions. We also compare to using a network to clean up reconstructions generated by backprojection and filtered backprojection, and find that this simple stretching procedure also gives lower mean squared error on previously unseen images

DDGM: Solving inverse problems by Diffusive Denoising of Gradient-based Minimization

Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a singular value decomposition of the forward operator, and several others backpropagate through the denoising net at runtime. Here we propose a simpler approach that combines the traditional gradient-based minimization of reconstruction error with denoising. Noise is also added at each step, so the iterative dynamics resembles a Langevin or diffusion process. Both the level of added noise and the size of the denoising step decay exponentially with time. We apply our method to the problem of tomographic reconstruction from electron micrographs acquired at multiple tilt angles. With empirical studies using simulated tilt views, we find parameter settings for our method that produce good results. We show that high accuracy can be achieved with as few as 50 denoising steps. We also compare with DDRM and DPS, more complex diffusion methods of the kinds mentioned above. These methods are less accurate (as measured by MSE and SSIM) for our tomography problem, even after the generation hyperparameters are optimized. Finally we extend our method to reconstruction of arbitrary-sized images and show results on 128 $\times$ 1568 pixel imagesComment: Solving inverse problems using gradient minimization coupled with a diffusion prio

Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift

Non-magnetic impurities in an S=1/2 Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, S_imp(k), measured in neutron scattering and the local susceptibility, chi_i measured in Knight shift experiments. S_imp(k) becomes quite large near the antiferromagnetic wave-vector, and exhibits much stronger temperature dependence than the bulk structure function. \chi_i has a large component which alternates and increases as a function of distance from the impurity.Comment: 8 pages (revtex) + one postscript file with 6 figures. A complete postscript file with all figures + text (10pages) is available from http://fy.chalmers.se/~eggert/struct.ps or by request from [email protected] Submitted to Phys. Rev. Let

Comparison of distance measures for historical spelling variants

This paper describes the comparison of selected distance measures in their applicability for supporting retrieval of historical spelling variants (hsv). The interdisciplinary project Rule-based search in text databases with nonstandard orthography develops a fuzzy fulltext search engine for historical text documents. This engine should provide easier text access for experts as well as interested amateurs. The FlexMetric framework enhances the distance measure algorithm found to be most efficient according to the results of the evaluation. This measure can be used for multiple applications, including searching, post-ranking, transformation and even reflection about one’s own language.IFIP International Conference on Artificial Intelligence in Theory and Practice - Speech and Natural LanguageRed de Universidades con Carreras en Informática (RedUNCI

Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain

Highly accurate results are presented for the susceptibility, $\chi (T)$ of the $s=1/2$ Heisenberg antiferromagnetic chain for all temperatures, using the Bethe ansatz and field theory methods. After going through a rounded peak, $\chi (T)$ approaches its asympotic zero-temperature value with infinite slope.Comment: 8 pages and 3 postscript figures appended (uuencoded), Revtex, Report #:UBCTP-94-00

Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators

Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-1/2 chain is calculated numerically in the presence of a next nearest neighbor coupling J2 for chains of up to 32 sites. By varying the coupling strength J2 we can control the effect of the marginal operator, and our results unambiguously confirm the field theory predictions. The critical value at which the marginal operator vanishes has been determined to be at J2 = 0.241167 +/- 0.000005J.Comment: revised paper with extended data-analysis. 5 pages, using revtex with 4 embedded figures (included with macro). A complete postscript file with all figures + text (5 pages) is available from http://FY.CHALMERS.SE/~eggert/marginal.ps or by request from [email protected]

MODELING AN ION EXCHANGE PROCESS FOR CESIUM REMOVAL FROM ALKALINE RADIOACTIVE WASTE SOLUTIONS

The performance of spherical Resorcinol-Formaldehyde ion-exchange resin for the removal of cesium from alkaline radioactive waste solutions has been investigated through computer modeling. Cesium adsorption isotherms were obtained by fitting experimental data using a thermodynamic framework. Results show that ion-exchange is an efficient method for cesium removal from highly alkaline radioactive waste solutions. On average, two 1300 liter columns operating in series are able to treat 690,000 liters of waste with an initial cesium concentration of 0.09 mM in 11 days achieving a decontamination factor of over 50,000. The study also tested the sensitivity of ion-exchange column performance to variations in flow rate, temperature and column dimensions. Modeling results can be used to optimize design of the ion exchange system