C. Mistretta, O. Wieben, J. Velikina, Y. Wu, K. Johnson, F. Korosec, O. Unal, G. Chen, S. Fain, B. Christian, O. Nalcioglu, R. Kruger, W. Block, A. Samsonov, M. Speidel, M. Van Lysel, H. Rowley, M. Supanich, P. Turski, Yan Wu, J. Holmes, S. Kecskemeti, C. Moran, R. O'Halloran, L. Keith, A. Alexander, E. Brodsky, J. Lee, T. Hall, J. Zagzebski
KEYWORDS: Signal to noise ratio, Composites, Image processing, X-rays, Magnetic resonance imaging, Medical imaging, Lawrencium, Convolution, Angiography, Positron emission tomography
During the last eight years our group has developed radial acquisitions with angular undersampling
factors of several hundred that accelerate MRI in selected applications. As with all previous
acceleration techniques, SNR typically falls as least as fast as the inverse square root of the
undersampling factor. This limits the SNR available to support the small voxels that these methods
can image over short time intervals in applications like time-resolved contrast-enhanced MR
angiography (CE-MRA). Instead of processing each time interval independently, we have developed
constrained reconstruction methods that exploit the significant correlation between temporal
sampling points. A broad class of methods, termed HighlY Constrained Back PRojection (HYPR),
generalizes this concept to other modalities and sampling dimensions.
In tomosynthesis, cone-beam projection data are acquired from a
few of view angles, which are not sufficient for an exact
reconstruction of an image object using state-of-the-art image
reconstruction algorithms. In the case of parallel-beam
projections, the well-known projection-slice theorem may be
utilized to transform the parallel-beam projections into the
Fourier space of an image object. Due to the limited range of view
angles, the available projection data can only populate a portion
of Fourier space. Moreover, the angular sampling rate of the
populated portion of the Fourier space may not satisfy the Nyquist
criterion. Thus, reconstructed images using direct Fourier
inversion contain severe streaking and distortion artifacts. In
this paper, we present a novel image reconstruction method via
minimizing the total variation (TV) of the reconstructed image for
limited view angle X-ray computed tomography. Specifically, the
missing data points in Fourier space, due to either the limited
range or undersampling of view angles, are iteratively filled
using the following two constraint conditions: (1) the total
variation of the reconstructed image is minimized and (2)
reconstructed image maintains fidelity to the sampled data in the
Fourier space. Using analytical phantoms, numerical simulations
were conducted to validate the new image reconstruction method.
Images are compared with two other image reconstruction methods in
terms of image artifact level and noise properties. Numerical
results demonstrated that the new image reconstruction algorithm
is superior to direct Fourier inversion reconstruction algorithm
and the projection onto convex sets (POCS) image reconstruction
algorithm.
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