Segmentation-free x-ray energy spectrum estimation for computed tomography

X-ray energy spectrum plays an essential role in imaging and related tasks. Due to the high photon flux of clinical CT scanners, most of the spectrum estimation methods are indirect and are usually suffered from various limitations. The recently proposed indirect transmission measurement-based method requires at least the segmentation of one material, which is insufficient for CT images of highly noisy and with artifacts. To combat for the bottleneck of spectrum estimation using segmented CT images, in this study, we develop a segmentation-free indirect transmission measurement based energy spectrum estimation method using dual-energy material decomposition. The general principle of the method is to compare polychromatic forward projection with raw projection to calibrate a set of unknown weights which are used to express the unknown spectrum together with a set of model spectra. After applying dual-energy material decomposition using high- and low-energy raw projection data, polychromatic forward projection is conducted on material-specific images. The unknown weights are then iteratively updated to minimize the difference between the raw projection and estimated projection. Both numerical simulations and experimental head phantom are used to evaluate the proposed method. The results indicate that the method provides accurate estimate of the spectrum and it may be attractive for dose calculations, artifacts correction and other clinical applications.Comment: 7 pages, 5 figure

Gram filtering and sinogram interpolation for pixel-basis in parallel-beam X-ray CT reconstruction

The key aspect of parallel-beam X-ray CT is forward and back projection, but its computational burden continues to be an obstacle for applications. We propose a method to improve the performance of related algorithms by calculating the Gram filter exactly and interpolating the sinogram signal optimally. In addition, the detector blur effect can be included in our model efficiently. The improvements in speed and quality for back projection and iterative reconstruction are shown in our experiments on both analytical phantoms and real CT images

ToTEM: The Bank of Canada's New Projection and Policy-Analysis Model

The Terms-of-Trade Economic Model, or ToTEM, replaced the Quarterly Projection Model (QPM) in December 2005 as the Bank's principal projection and policy-analysis model for the Canadian economy. Benefiting from advances in economic modelling and computer power, ToTEM builds on the strengths of QPM, allowing for optimizing behaviour on the part of firms and households, both in and out of steady state, in a multi-product environment. The authors explain the motivation behind the development of ToTEM, provide an overview of the model and its calibration, and present several simulations to illustrate its key properties, concluding with some indications of how the model is expected to evolve going forward.

Mono3D++: Monocular 3D Vehicle Detection with Two-Scale 3D Hypotheses and Task Priors

We present a method to infer 3D pose and shape of vehicles from a single image. To tackle this ill-posed problem, we optimize two-scale projection consistency between the generated 3D hypotheses and their 2D pseudo-measurements. Specifically, we use a morphable wireframe model to generate a fine-scaled representation of vehicle shape and pose. To reduce its sensitivity to 2D landmarks, we jointly model the 3D bounding box as a coarse representation which improves robustness. We also integrate three task priors, including unsupervised monocular depth, a ground plane constraint as well as vehicle shape priors, with forward projection errors into an overall energy function.Comment: Proc. of the AAAI, September 201

Smooth K-Theory

We construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-forward which satisfies functoriality, compatibility with pull-back diagrams, and projection and bordism formulas. We construct a multiplicative lift of the Chern character from smooth K-theory to smooth rational cohomology and verify that the cohomological version of the Atiyah-Singer index theorem for families lifts to smooth cohomology.Comment: v4 93 pages, version to appear in Asterisque (Bismut 60 proceedings

The Shell Model, the Renormalization Group and the Two-Body Interaction

The no-core shell model and the effective interaction $V_{{\rm low} k}$ can both be derived using the Lee-Suzuki projection operator formalism. The main difference between the two is the choice of basis states that define the model space. The effective interaction $V_{{\rm low} k}$ can also be derived using the renormalization group. That renormalization group derivation can be extended in a straight forward manner to also include the no-core shell model. In the nuclear matter limit the no-core shell model effective interaction in the two-body approximation reduces identically to $V_{{\rm low} k}$. The same considerations apply to the Bloch-Horowitz version of the shell model and the renormalization group treatment of two-body scattering by Birse, McGovern and Richardson

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed

The Heston stochastic volatility model in Hilbert space

We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process is then defined by a Cholesky decomposition of the variance process. We define a Hilbert-valued Ornstein-Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional and covariance operator of this process. This process is then applied to the modelling of forward curves in energy markets. Finally, we compute the dynamics of the tensor Heston volatility model when the generator is bounded, and study its projection down to the real line for comparison with the classical Heston dynamics