X-ray Fluorescence Sectioning

In this paper, we propose an x-ray fluorescence imaging system for elemental analysis. The key idea is what we call "x-ray fluorescence sectioning". Specifically, a slit collimator in front of an x-ray tube is used to shape x-rays into a fan-beam to illuminate a planar section of an object. Then, relevant elements such as gold nanoparticles on the fan-beam plane are excited to generate x-ray fluorescence signals. One or more 2D spectral detectors are placed to face the fan-beam plane and directly measure x-ray fluorescence data. Detector elements are so collimated that each element only sees a unique area element on the fan-beam plane and records the x-ray fluorescence signal accordingly. The measured 2D x-ray fluorescence data can be refined in reference to the attenuation characteristics of the object and the divergence of the beam for accurate elemental mapping. This x-ray fluorescence sectioning system promises fast fluorescence tomographic imaging without a complex inverse procedure. The design can be adapted in various ways, such as with the use of a larger detector size to improve the signal to noise ratio. In this case, the detector(s) can be shifted multiple times for image deblurring

Monochromatic CT Image Reconstruction from Current-Integrating Data via Deep Learning

In clinical CT, the x-ray source emits polychromatic x-rays, which are detected in the current-integrating mode. This physical process is accurately described by an energy-dependent non-linear integral model on the basis of the Beer-Lambert law. However, the non-linear model is too complicated to be directly solved for the image reconstruction, and is often approximated to a linear integral model in the form of the Radon transform, basically ignoring energy-dependent information. This model approximation would generate inaccurate quantification of attenuation image and significant beam-hardening artifacts. In this paper, we develop a deep-learning-based CT image reconstruction method to address the mismatch of computing model to physical model. Our method learns a nonlinear transformation from big data to correct measured projection data to accurately match the linear integral model, realize monochromatic imaging and overcome beam hardening effectively. The deep-learning network is trained and tested using clinical dual-energy dataset to demonstrate the feasibility of the proposed methodology. Results show that the proposed method can achieve a high accuracy of the projection correction with a relative error of less than 0.2%

Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits

Lyapunov exponents of a hyperbolic ergodic measure are approximated by Lyapunov exponents of hyperbolic atomic measures on periodic orbits

Continuity of entropy map for nonuniformly hyperbolic systems

We prove that entropy map is upper semi-continuous for C1 nonuniformly hyperbolic systems with domination, while it is not true for C1+alpha nonuniformly hyperbolic systems in general. This goes a little against a common intuition that conclusions are parallel between C1+domination systems and C1+alpha systems.Comment: 15 pages, 2 figure

Modulated Luminescent Tomography

We propose and analyze a mathematical model of Modulated Luminescent Tomography. We show that when single X-rays or focused X-rays are used as an excitation, the problem is similar to the inversion of weighted X-ray transforms. In particular, we give an explicit inversion in the case of Dual Cone X-ray excitation

General Backpropagation Algorithm for Training Second-order Neural Networks

The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to 2nd order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single 2nd order neurons already has a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation (BP) algorithm to train the network consisting of 2nd-order neurons. The numerical studies are performed to verify of the generalized BP algorithm.Comment: 5 pages, 7 figures, 19 reference

Fourier transform based iterative method for x-ray differential phase-contrast computed tomography

Biological soft tissues encountered in clinical and pre-clinical imaging mainly consist of light element atoms, and their composition is nearly uniform with little density variation. Thus, x-ray attenuation imaging suffers from low image contrast resolution. By contrast, x-ray phase shift of soft tissues is about a thousand times greater than x-ray absorption over the diagnostic energy range, thereby a significantly higher sensitivity can be achieved in terms of phase shift. In this paper, we propose a novel Fourier transform based iterative method to perform x-ray tomographic imaging of the refractive index directly from differential phase shift data. This approach offers distinct advantages in cases of incomplete and noisy data than analytic reconstruction, and especially suitable for phase-contrast interior tomography by incorporating prior knowledge in a region of interest (ROI). Biological experiments demonstrate the merits of the proposed approach

Low complexity resource allocation for load minimization in OFDMA wireless networks

To cope with the ever increasing demand for bandwidth, future wireless networks will be designed with reuse distance equal to one. This scenario requires the implementation of techniques able to manage the strong multiple access interference each cell generates towards its neighbor cells. In particular, low complexity and reduced feedback are important requirements for practical algorithms. In this paper we study an allocation problem for OFDMA networks formulated with the objective of minimizing the load of each cell in the system subject to the constraint that each user meets its target rate. We decompose resource allocation into two sub-problems: channel allocation under deterministic power assignment and continuous power assignment optimization. Channel allocation is formulated as the problem of finding the maximum weighted independent set (MWIS) in graph theory. In addition, we propose a minimal weighted-degree greedy (MWDG) algorithm of which the approximation factor is analyzed. For power allocation, an iterative power reassignment algorithm (DPRA) is proposed. The control information requested to perform the allocation is limited and the computational burden is shared between the base station and the user equipments. Simulations have been carried out under constant bit rate traffic model and the results have been compared with other allocation schemes of similar complexity. MWDG has excellent performance and outperforms all other techniques.Comment: 24 pages, 8 figure

Projection Decomposition for Dual-energy Computed Tomography

Dual-energy computed tomography (CT) is to reconstruct images of an object from two projection datasets generated from two distinct x-ray source energy spectra. It can provide more accurate attenuation quantification than conventional CT with a single x-ray energy spectrum. In the diagnostic energy range, x-ray energy-dependent attenuation can be approximated as a linear combination of photoelectric absorption and Compton scattering. Hence, two physical components of x-ray attenuation can be determined from two spectral informative projection datasets to achieve monochromatic imaging and material decomposition. In this paper, a projection decomposition method is proposed for the image reconstruction in dual-energy CT. This method combines both an analytical algorithm and a single-variable optimization method to solve the non-linear polychromatic x-ray integral model, allowing accurate quantification of photoelectric absorption and Compton scattering components. Numerical tests are performed to illustrate the merit of the proposed method by comparing with classical projection decomposition methods

Top-level Design and Pilot Analysis of Low-end CT Scanners Based on Linear Scanning for Developing Countries

Purpose: The goal is to develop a new architecture for computed tomography (CT) which is at an ultra-low-dose for developing countries, especially in rural areas. Methods: The proposed scheme is inspired by the recently developed compressive sensing and interior tomography techniques, where the data acquisition system targets a region of interest (ROI) to acquire limited and truncated data. The source and detector are translated in opposite directions for either ROI reconstruction with one or more localized linear scans or global reconstruction by combining multiple ROI reconstructions. In other words, the popular slip ring is replaced by a translation based setup, and the instrumentation cost is reduced by a relaxation of the imaging speed requirement. Results: The various translational scanning modes are theoretically analyzed, and the scanning parameters are optimized. The numerical simulation results from different numbers of linear scans confirm the feasibility of the proposed scheme, and suggest two preferred low-end systems for horizontal and vertical patient positions respectively. Conclusion: Ultra-low-cost x-ray CT is feasible with our proposed combination of linear scanning, compressive sensing, and interior tomography. The proposed architecture can be tailored into permanent, movable, or reconfigurable systems as desirable. Advanced image registration and spectral imaging features can be included as well.Comment: 19 pages, 10 figure