2,110 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
Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization
We explore the use of the recently proposed "total nuclear variation" (TNV)
as a regularizer for reconstructing multi-channel, spectral CT images. This
convex penalty is a natural extension of the total variation (TV) to
vector-valued images and has the advantage of encouraging common edge locations
and a shared gradient direction among image channels. We show how it can be
incorporated into a general, data-constrained reconstruction framework and
derive update equations based on the first-order, primal-dual algorithm of
Chambolle and Pock. Early simulation studies based on the numerical XCAT
phantom indicate that the inter-channel coupling introduced by the TNV leads to
better preservation of image features at high levels of regularization,
compared to independent, channel-by-channel TV reconstructions.Comment: Submitted to Physics in Medicine and Biolog
Coherence retrieval using trace regularization
The mutual intensity and its equivalent phase-space representations quantify
an optical field's state of coherence and are important tools in the study of
light propagation and dynamics, but they can only be estimated indirectly from
measurements through a process called coherence retrieval, otherwise known as
phase-space tomography. As practical considerations often rule out the
availability of a complete set of measurements, coherence retrieval is usually
a challenging high-dimensional ill-posed inverse problem. In this paper, we
propose a trace-regularized optimization model for coherence retrieval and a
provably-convergent adaptive accelerated proximal gradient algorithm for
solving the resulting problem. Applying our model and algorithm to both
simulated and experimental data, we demonstrate an improvement in
reconstruction quality over previous models as well as an increase in
convergence speed compared to existing first-order methods.Comment: 28 pages, 10 figures, accepted for publication in SIAM Journal on
Imaging Science
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