1,367 research outputs found
Autocalibrating and Calibrationless Parallel Magnetic Resonance Imaging as a Bilinear Inverse Problem
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit
the spatially varying sensitivity profiles of receive-coil arrays as additional
source of information. This allows to reduce the number of time-consuming
Fourier-encoding steps by undersampling. The receive sensitivities are a priori
unknown and influenced by geometry and electric properties of the (moving)
subject. For optimal results, they need to be estimated jointly with the image
from the same undersampled measurement data. Formulated as an inverse problem,
this leads to a bilinear reconstruction problem related to multi-channel blind
deconvolution. In this work, we will discuss some recently developed approaches
for the solution of this problem.Comment: 3 pages, 3 figures, 12th International Conference on Sampling Theory
and Applications, Tallinn 201
Aggregated motion estimation for real-time MRI reconstruction
Real-time magnetic resonance imaging (MRI) methods generally shorten the
measuring time by acquiring less data than needed according to the sampling
theorem. In order to obtain a proper image from such undersampled data, the
reconstruction is commonly defined as the solution of an inverse problem, which
is regularized by a priori assumptions about the object. While practical
realizations have hitherto been surprisingly successful, strong assumptions
about the continuity of image features may affect the temporal fidelity of the
estimated images. Here we propose a novel approach for the reconstruction of
serial real-time MRI data which integrates the deformations between nearby
frames into the data consistency term. The method is not required to be affine
or rigid and does not need additional measurements. Moreover, it handles
multi-channel MRI data by simultaneously determining the image and its coil
sensitivity profiles in a nonlinear formulation which also adapts to
non-Cartesian (e.g., radial) sampling schemes. Experimental results of a motion
phantom with controlled speed and in vivo measurements of rapid tongue
movements demonstrate image improvements in preserving temporal fidelity and
removing residual artifacts.Comment: This is a preliminary technical report. A polished version is
published by Magnetic Resonance in Medicine. Magnetic Resonance in Medicine
201
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial
frequency domain (k-space), typically by time-consuming line-by-line scanning
on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of
data using multiple receivers (parallel imaging), and by using more efficient
non-Cartesian sampling schemes. As shown here, reconstruction from samples at
arbitrary locations can be understood as approximation of vector-valued
functions from the acquired samples and formulated using a Reproducing Kernel
Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial
sensitivities of the receive coils. This establishes a formal connection
between approximation theory and parallel imaging. Theoretical tools from
approximation theory can then be used to understand reconstruction in k-space
and to extend the analysis of the effects of samples selection beyond the
traditional g-factor noise analysis to both noise amplification and
approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure
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