38,288 research outputs found
Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization
We present a reconstruction method involving maximum-likelihood expectation
maximization (MLEM) to model Poisson noise as applied to fluorescence molecular
tomography (FMT). MLEM is initialized with the output from a sparse
reconstruction-based approach, which performs truncated singular value
decomposition-based preconditioning followed by fast iterative
shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation
for this approach is that sparsity information could be accounted for within
the initialization, while MLEM would accurately model Poisson noise in the FMT
system. Simulation experiments show the proposed method significantly improves
images qualitatively and quantitatively. The method results in over 20 times
faster convergence compared to uniformly initialized MLEM and improves
robustness to noise compared to pure sparse reconstruction. We also
theoretically justify the ability of the proposed approach to reduce noise in
the background region compared to pure sparse reconstruction. Overall, these
results provide strong evidence to model Poisson noise in FMT reconstruction
and for application of the proposed reconstruction framework to FMT imaging
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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