8,481 research outputs found
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
k-Space Deep Learning for Reference-free EPI Ghost Correction
Nyquist ghost artifacts in EPI are originated from phase mismatch between the
even and odd echoes. However, conventional correction methods using reference
scans often produce erroneous results especially in high-field MRI due to the
non-linear and time-varying local magnetic field changes. Recently, it was
shown that the problem of ghost correction can be reformulated as k-space
interpolation problem that can be solved using structured low-rank Hankel
matrix approaches. Another recent work showed that data driven Hankel matrix
decomposition can be reformulated to exhibit similar structures as deep
convolutional neural network. By synergistically combining these findings, we
propose a k-space deep learning approach that immediately corrects the phase
mismatch without a reference scan in both accelerated and non-accelerated EPI
acquisitions. To take advantage of the even and odd-phase directional
redundancy, the k-space data is divided into two channels configured with even
and odd phase encodings. The redundancies between coils are also exploited by
stacking the multi-coil k-space data into additional input channels. Then, our
k-space ghost correction network is trained to learn the interpolation kernel
to estimate the missing virtual k-space data. For the accelerated EPI data, the
same neural network is trained to directly estimate the interpolation kernels
for missing k-space data from both ghost and subsampling. Reconstruction
results using 3T and 7T in-vivo data showed that the proposed method
outperformed the image quality compared to the existing methods, and the
computing time is much faster.The proposed k-space deep learning for EPI ghost
correction is highly robust and fast, and can be combined with acceleration, so
that it can be used as a promising correction tool for high-field MRI without
changing the current acquisition protocol.Comment: To appear in Magnetic Resonance in Medicin
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
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