Model-based iterative reconstruction (MBIR) methods based on maximum a posteriori (MAP) estimation have been
recently introduced to multi-slice CT scanners. The model-based approach has shown promising image quality
improvement with reduced radiation dose compared to conventional FBP methods, but the associated high computation
cost limits its widespread use in clinical environments. Among the various choices of numerical algorithms to optimize
the MAP cost function, simultaneous update methods such as the conjugate gradient (CG) method have a relatively high
level of parallelism to take full advantage of a new generation of many-core computing hardware. With proper
preconditioning techniques, fast convergence speeds of CG algorithms have been demonstrated in 3D emission and 2D
transmission reconstruction. However, 3D transmission reconstruction using preconditioned conjugate gradient (PCG)
has not been reported. Additional challenges in applying PCG in 3D CT reconstruction include the large size of clinical
CT data, shift-variant and incomplete sampling, and complex regularization schemes to meet the diagnostic standard of
image quality. In this paper, we present a ramp-filter based PCG algorithm for 3D CT MBIR. Convergence speeds of
algorithms with and without using the preconditioner are compared.
Bayesian estimation is a statistical approach for incorporating prior information through the choice of an a
priori distribution for a random field. A priori image models in Bayesian image estimation are typically low-order
Markov random fields (MRFs), effectively penalizing only differences among immediately neighboring
voxels. This limits spectral description to a crude low-pass model. For applications where more flexibility in
spectral response is desired, potential benefit exists in models which accord higher a priori probability to content
in higher frequencies. Our research explores the potential of larger neighborhoods in MRFs to raise the number
of degrees of freedom in spectral description. Similarly to classical filter design, the MRF coefficients may be
chosen to yield a desired pass-band/stop-band characteristic shape in the a priori model of the images. In this
paper, we present an alternative design method, where high-quality sample images are used to estimate the MRF
coefficients by fitting them into the spatial correlation of the given ensemble. This method allows us to choose
weights that increase the probability of occurrence of strong components at particular spatial frequencies. This
allows direct adaptation of the MRFs for different tissue types based on sample images with different frequency
content. In this paper, we consider particularly the preservation of detail in bone structure in X-ray CT. Our
results show that MRF design can be used to obtain bone emphasis similar to that of conventional filtered
back-projection (FBP) with a bone kernel.
Model based iterative reconstruction (MBIR) algorithms have recently been applied to computed tomography and
demonstrated superior image quality. This algorithmic framework also provides us the flexibility to incorporate
more sophisticated models of the data acquisition process. In this paper, we present the kinetic parameter
iterative reconstruction (KPIR) algorithm which estimates voxel values as a function of time in the MBIR
framework. We introduce a parametric kinetic model for each voxel, and estimate the kinetic parameters directly
from the data. Results on phantom study and clinical data show that the proposed method can significantly
reduce motion artifacts in the reconstruction.
Medical imaging typically requires the reconstruction of a limited region of interest (ROI) to obtain a high
resolution image of the anatomy of interest. Although targeted reconstruction is straightforward for analytical
reconstruction methods, it is more complicated for statistical iterative techniques, which must reconstruct all
objects in the field of view (FOV) to account for all sources of attenuation along the ray paths from x-ray
source to detector. A brute force approach would require the reconstruction of the full field of view in high-resolution,
but with prohibitive computational cost. In this paper, we propose a multi-resolution approach to
accelerate targeted iterative reconstruction using the non-homogeneous ICD (NH-ICD) algorithm. NH-ICD aims
at speeding up convergence of the coordinate descent algorithm by selecting preferentially those voxels most in
need of updating. To further optimize ROI reconstruction, we use a multi-resolution approach which combines
three separate improvements. First, we introduce the modified weighted NH-ICD algorithm, which weights the
pixel selection criteria according to the position of the voxel relative to the ROI to speed up convergence within
the ROI. Second, we propose a simple correction to the error sinogram to correct for inconsistencies between
resolutions when the forward model is not scale invariant. Finally, we leverage the flexibility of the ICD algorithm
to add selected edge pixels outside the ROI to the ROI reconstruction in order to minimize transition artifacts
at the ROI boundary. Experiments on clinical data illustrate how each component of the method improves
convergence speed and image quality.
Statistical reconstruction methods show great promise for improving resolution, and reducing noise and artifacts
in helical X-ray CT. In fact, statistical reconstruction seems to be particularly valuable in maintaining reconstructed
image quality when the dosage is low and the noise is therefore high. However, high computational
cost and long reconstruction times remain as a barrier to the use of statistical reconstruction in practical applications.
Among the various iterative methods that have been studied for statistical reconstruction, iterative
coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its
fast convergence.
This paper presents a novel method for further speeding the convergence of the ICD algorithm, and therefore
reducing the overall reconstruction time for statistical reconstruction. The method, which we call nonhomogeneous
iterative coordinate descent (NH-ICD) uses spatially non-homogeneous updates to speed convergence
by focusing computation where it is most needed. Experimental results with real data indicate that the
method speeds reconstruction by roughly a factor of two for typical 3D multi-slice geometries.
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