48,553 research outputs found
High resolution in-vivo MR-STAT using a matrix-free and parallelized reconstruction algorithm
MR-STAT is a recently proposed framework that allows the reconstruction of
multiple quantitative parameter maps from a single short scan by performing
spatial localisation and parameter estimation on the time domain data
simultaneously, without relying on the FFT. To do this at high-resolution,
specialized algorithms are required to solve the underlying large-scale
non-linear optimisation problem. We propose a matrix-free and parallelized
inexact Gauss-Newton based reconstruction algorithm for this purpose. The
proposed algorithm is implemented on a high performance computing cluster and
is demonstrated to be able to generate high-resolution (
in-plane resolution) quantitative parameter maps in simulation, phantom and
in-vivo brain experiments. Reconstructed and values for the gel
phantoms are in agreement with results from gold standard measurements and for
the in-vivo experiments the quantitative values show good agreement with
literature values. In all experiments short pulse sequences with robust
Cartesian sampling are used for which conventional MR Fingerprinting
reconstructions are shown to fail.Comment: Accepted by NMR in Biomedicine on 2019-12-0
Quantitative photoacoustic tomography with piecewise constant material parameters
The goal of quantitative photoacoustic tomography is to determine optical and
acoustical material properties from initial pressure maps as obtained, for
instance, from photoacoustic imaging. The most relevant parameters are
absorption, diffusion and Grueneisen coefficients, all of which can be
heterogeneous. Recent work by Bal and Ren shows that in general, unique
reconstruction of all three parameters is impossible, even if multiple
measurements of the initial pressure (corresponding to different laser
excitation directions at a single wavelength) are available.
Here, we propose a restriction to piecewise constant material parameters. We
show that in the diffusion approximation of light transfer, piecewise constant
absorption, diffusion and Gr\"uneisen coefficients can be recovered uniquely
from photoacoustic measurements at a single wavelength. In addition, we
implemented our ideas numerically and tested them on simulated
three-dimensional data
A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
In this article, we consider the inverse problem of determining spatially
heterogeneous absorption and diffusion coefficients from a single measurement
of the absorbed energy (in the steady-state diffusion approximation of light
transfer). This problem, which is central in quantitative photoacoustic
tomography, is in general ill-posed since it admits an infinite number of
solution pairs. We show that when the coefficients are known to be piecewise
constant functions, a unique solution can be obtained. For the numerical
determination of the coefficients, we suggest a variational method based based
on an Ambrosio-Tortorelli-approximation of a Mumford-Shah-like functional,
which we implemented numerically and tested on simulated two-dimensional data
A Novel Self-Intersection Penalty Term for Statistical Body Shape Models and Its Applications in 3D Pose Estimation
Statistical body shape models are widely used in 3D pose estimation due to
their low-dimensional parameters representation. However, it is difficult to
avoid self-intersection between body parts accurately. Motivated by this fact,
we proposed a novel self-intersection penalty term for statistical body shape
models applied in 3D pose estimation. To avoid the trouble of computing
self-intersection for complex surfaces like the body meshes, the gradient of
our proposed self-intersection penalty term is manually derived from the
perspective of geometry. First, the self-intersection penalty term is defined
as the volume of the self-intersection region. To calculate the partial
derivatives with respect to the coordinates of the vertices, we employed
detection rays to divide vertices of statistical body shape models into
different groups depending on whether the vertex is in the region of
self-intersection. Second, the partial derivatives could be easily derived by
the normal vectors of neighboring triangles of the vertices. Finally, this
penalty term could be applied in gradient-based optimization algorithms to
remove the self-intersection of triangular meshes without using any
approximation. Qualitative and quantitative evaluations were conducted to
demonstrate the effectiveness and generality of our proposed method compared
with previous approaches. The experimental results show that our proposed
penalty term can avoid self-intersection to exclude unreasonable predictions
and improves the accuracy of 3D pose estimation indirectly. Further more, the
proposed method could be employed universally in triangular mesh based 3D
reconstruction
Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulation
Ultrasound-modulated optical tomography is an emerging biomedical imaging
modality which uses the spatially localised acoustically-driven modulation of
coherent light as a probe of the structure and optical properties of biological
tissues. In this work we begin by providing an overview of forward modelling
methods, before deriving a linearised diffusion-style model which calculates
the first-harmonic modulated flux measured on the boundary of a given domain.
We derive and examine the correlation measurement density functions of the
model which describe the sensitivity of the modality to perturbations in the
optical parameters of interest. Finally, we employ said functions in the
development of an adjoint-assisted gradient based image reconstruction method,
which ameliorates the computational burden and memory requirements of a
traditional Newton-based optimisation approach. We validate our work by
performing reconstructions of optical absorption and scattering in two- and
three-dimensions using simulated measurements with 1% proportional Gaussian
noise, and demonstrate the successful recovery of the parameters to within
+/-5% of their true values when the resolution of the ultrasound raster probing
the domain is sufficient to delineate perturbing inclusions.Comment: 12 pages, 6 figure
Accuracy of spike-train Fourier reconstruction for colliding nodes
We consider Fourier reconstruction problem for signals F, which are linear
combinations of shifted delta-functions. We assume the Fourier transform of F
to be known on the frequency interval [-N,N], with an absolute error not
exceeding e > 0. We give an absolute lower bound (which is valid with any
reconstruction method) for the "worst case" reconstruction error of F in
situations where the nodes (i.e. the positions of the shifted delta-functions
in F) are known to form an l elements cluster of a size h << 1. Using
"decimation" reconstruction algorithm we provide an upper bound for the
reconstruction error, essentially of the same form as the lower one. Roughly,
our main result states that for N*h of order of (2l-1)-st root of e the worst
case reconstruction error of the cluster nodes is of the same order as h, and
hence the inside configuration of the cluster nodes (in the worst case
scenario) cannot be reconstructed at all. On the other hand, decimation
algorithm reconstructs F with the accuracy of order of 2l-st root of e
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