29,447 research outputs found
Incorporating Relaxivities to More Accurately Reconstruct MR Images
Purpose
To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.
Materials and methods
In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2⁎, T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2⁎, ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2⁎, T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects.
Result
Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations.
Conclusion
With the use of the proposed method, the effects of T2⁎ and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration
Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions
Boltzmann sampling is commonly used to uniformly sample objects of a
particular size from large combinatorial sets. For this technique to be
effective, one needs to prove that (1) the sampling procedure is efficient and
(2) objects of the desired size are generated with sufficiently high
probability. We use this approach to give a provably efficient sampling
algorithm for a class of weighted integer partitions related to Bose-Einstein
condensation from statistical physics. Our sampling algorithm is a
probabilistic interpretation of the ordinary generating function for these
objects, derived from the symbolic method of analytic combinatorics. Using the
Khintchine-Meinardus probabilistic method to bound the rejection rate of our
Boltzmann sampler through singularity analysis of Dirichlet generating
functions, we offer an alternative approach to analyze Boltzmann samplers for
objects with multiplicative structure.Comment: 20 pages, 1 figur
A Survey on Software Testing Techniques using Genetic Algorithm
The overall aim of the software industry is to ensure delivery of high
quality software to the end user. To ensure high quality software, it is
required to test software. Testing ensures that software meets user
specifications and requirements. However, the field of software testing has a
number of underlying issues like effective generation of test cases,
prioritisation of test cases etc which need to be tackled. These issues demand
on effort, time and cost of the testing. Different techniques and methodologies
have been proposed for taking care of these issues. Use of evolutionary
algorithms for automatic test generation has been an area of interest for many
researchers. Genetic Algorithm (GA) is one such form of evolutionary
algorithms. In this research paper, we present a survey of GA approach for
addressing the various issues encountered during software testing.Comment: 13 Page
Adiabatic stability under semi-strong interactions: The weakly damped regime
We rigorously derive multi-pulse interaction laws for the semi-strong
interactions in a family of singularly-perturbed and weakly-damped
reaction-diffusion systems in one space dimension. Most significantly, we show
the existence of a manifold of quasi-steady N-pulse solutions and identify a
"normal-hyperbolicity" condition which balances the asymptotic weakness of the
linear damping against the algebraic evolution rate of the multi-pulses. Our
main result is the adiabatic stability of the manifolds subject to this normal
hyperbolicity condition. More specifically, the spectrum of the linearization
about a fixed N-pulse configuration contains essential spectrum that is
asymptotically close to the origin as well as semi-strong eigenvalues which
move at leading order as the pulse positions evolve. We characterize the
semi-strong eigenvalues in terms of the spectrum of an explicit N by N matrix,
and rigorously bound the error between the N-pulse manifold and the evolution
of the full system, in a polynomially weighted space, so long as the
semi-strong spectrum remains strictly in the left-half complex plane, and the
essential spectrum is not too close to the origin
Modeling and forecasting electricity spot prices: A functional data perspective
Classical time series models have serious difficulties in modeling and
forecasting the enormous fluctuations of electricity spot prices. Markov regime
switch models belong to the most often used models in the electricity
literature. These models try to capture the fluctuations of electricity spot
prices by using different regimes, each with its own mean and covariance
structure. Usually one regime is dedicated to moderate prices and another is
dedicated to high prices. However, these models show poor performance and there
is no theoretical justification for this kind of classification. The merit
order model, the most important micro-economic pricing model for electricity
spot prices, however, suggests a continuum of mean levels with a functional
dependence on electricity demand. We propose a new statistical perspective on
modeling and forecasting electricity spot prices that accounts for the merit
order model. In a first step, the functional relation between electricity spot
prices and electricity demand is modeled by daily price-demand functions. In a
second step, we parameterize the series of daily price-demand functions using a
functional factor model. The power of this new perspective is demonstrated by a
forecast study that compares our functional factor model with two established
classical time series models as well as two alternative functional data models.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS652 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exact Meander Asymptotics: a Numerical Check
This note addresses the meander enumeration problem: "Count all topologically
inequivalent configurations of a closed planar non self-intersecting curve
crossing a line through a given number of points". We review a description of
meanders introduced recently in terms of the coupling to gravity of a
two-flavored fully-packed loop model. The subsequent analytic predictions for
various meandric configuration exponents are checked against exact enumeration,
using a transfer matrix method, with an excellent agreement.Comment: 48 pages, 24 figures, tex, harvmac, eps
Video Interpolation using Optical Flow and Laplacian Smoothness
Non-rigid video interpolation is a common computer vision task. In this paper
we present an optical flow approach which adopts a Laplacian Cotangent Mesh
constraint to enhance the local smoothness. Similar to Li et al., our approach
adopts a mesh to the image with a resolution up to one vertex per pixel and
uses angle constraints to ensure sensible local deformations between image
pairs. The Laplacian Mesh constraints are expressed wholly inside the optical
flow optimization, and can be applied in a straightforward manner to a wide
range of image tracking and registration problems. We evaluate our approach by
testing on several benchmark datasets, including the Middlebury and Garg et al.
datasets. In addition, we show application of our method for constructing 3D
Morphable Facial Models from dynamic 3D data
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