In this study we apply a total variation (TV) minimization algorithm to image reconstruction in magnetic
resonance imaging (MRI). This algorithm is particularly effective for underlying images that are approximately
piecewise constant. While the underlying proton spin density in MRI can satisfy this condition under certain
circumstances, it is often distorted by unavoidable physical factors that alter the phase of the complex image.
In this work, we employ a known method of removing this slow phase variation resulting from magnetic field
inhomogeneities to obtain a spin density distribution that is piecewise constant. After the phase removal, we
apply the TV minimization algorithm to obtain images from 20% of the full MRI data set.
An accurate method for evaluating the Hotelling observer for large linear systems is generalized.
The method involves solving an m-channel channelized Hotelling observer where the channels are
refined in an iterative manner. Challenging numerical examples are shown in order to illustrate
the method and give a sense of the convergence rates as a function of m.
We use a task-based study to objectively evaluate the effect of variable versus fixed focal length in determining
the position of a lesion in helical cone-beam computed tomography (HCBCT). This method will be used
to assess whether variable focal length CBCT scans provide a measurable improvement in estimating lesion
position relative to fixed focal length CBCT in diagnostic applications. In this simulation study a 1 cm diameter
spherical lesion is placed at four different positions within a three-dimensional Shepp-Logan head phantom. The
axial plane is taken to point along the z-axis, which is also the central axis of the helix. The lesion is placed at
the center of the Shepp-Logan phantom, at positions displaced ±5 cm in x, and at a position displaced 5 cm
in y. Four different scans of pitch length 10 cm are then performed using 128 views over 360° with a 100×300
pixel (20 cm×60 cm) detector. Two scans have a fixed focal length of 50 cm between the X-ray source and
the center of rotation (COR), varying only in the starting angle of the source (0° and 90°). We call this the
circular configuration. The other two scans have a variable focal length following the curvature of the head
phantom and ranging from 37.5 cm to 50 cm. We call this the elliptical configuration. The detector rotates
with the source but maintains a constant distance of 30 cm from the COR. A likelihood gridding technique
is used to assess bias and variance in the position estimates determined from each scan configuration. We
find that the biases are small relative to the variances, and have no apparent preferred direction. Of the 24
circular to elliptical comparisons made, we find that in 14 cases the elliptical scan has a smaller variance that
is statistically significant(p ≤ 0.05). By contrast, we find no statistically significant cases in which the circular
scan gives a smaller variance compared to the elliptical scan. We conclude that using a variable focal length
adapted to the contours of the head phantom provides more precise results, but caution that this is a limited
pilot study and many more factors will be accounted for in future work.
KEYWORDS: Signal to noise ratio, Reconstruction algorithms, Image restoration, Signal detection, Tomography, CT reconstruction, Detection and tracking algorithms, Data modeling, Systems modeling, Computed tomography
Signal detection by the channelized Hotelling (ch-Hotelling) observer is studied for tomographic
application by employing a small, tractable 2D model of a computed tomography (CT) system.
The primary goal of this manuscript is to develop a practical method for evaluating the ch-Hotelling
observer that can generalize to larger 3D cone-beam CT systems. The use of the ch-Hotelling observer for evaluating tomographic image reconstruction algorithms is also demonstrated. For a realistic model for CT, the ch-Hotelling observer can be a good approximation to the ideal observer.
The ch-Hotelling observer is applied to both the projection data and the reconstructed images. The difference in signal-to-noise ratio for signal detection in both of these domains provides a metric for evaluating the image reconstruction algorithm.
We present a method for obtaining accurate image reconstruction from sparsely sampled magnetic resonance
imaging (MRI) data obtained along spiral trajectories in Fourier space. This method minimizes the total
variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the image
matches the known samples in Fourier space. Using this method, we demonstrate accurate image reconstruction
from sparse Fourier samples. We also show that the algorithm is reasonably robust to the effects
of measurement noise. Reconstruction from such sparse sampling should reduce scan times, improving scan
quality through reduction of motion-related artifacts and allowing more rapid evaluation of time-critical
conditions such as stroke. Although our results are discussed in the context of two-dimensional MRI, they
are directly applicable to higher dimensional imaging and to other sampling patterns in Fourier space.
We present a total-variation (TV)-based method for obtaining accurate image reconstruction in diffraction
tomography (DT) from sparse data. Using computer-simulated data, we show that the TV-based method
is effective in reconstructing accurate images using a total number of data samples comparable to or less
than that of other current algorithms, such as filtered backpropagation or inverse scattering. Our algorithm
is robust to the effects of measurement noise, and performs very well in limited angle scans. Overall our results indicate that TV minimization can be applied to DT image reconstruction under a variety of scan configurations and data conditions.
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