Model-based image reconstruction (MBIR) methods for X-ray CT use accuratemodels of the CT acquisition process, the statistics of the noisy measurements,and noise-reducing regularization to produce potentially higher quality imagesthan conventional methods even at reduced X-ray doses.They do this byminimizing a statistically motivated high-dimensional cost function; the highcomputational cost of numerically minimizing this function has prevented MBIRmethods from reaching ubiquity in the clinic.Modern highly-parallel hardwarelike graphics processing units (GPUs) may offer the computational resources tosolve these reconstruction problems quickly, but simply ;;translating;; existingalgorithms designed for conventional processors to the GPU may not fullyexploit the hardware;;s capabilities.This thesis proposes GPU-specialized image denoising and image reconstructionalgorithms.The proposed image denoising algorithm uses group coordinatedescent with carefully structured groups.The algorithm converges veryrapidly: in one experiment, it denoises a 65 megapixel image in about 1.5seconds, while the popular Chambolle-Pock primal-dual algorithm running on thesame hardware takes over a minute to reach the same level of accuracy.For X-ray CT reconstruction, this thesis uses duality and group coordinateascent to propose an alternative to the popular ordered subsets (OS) method.Similar to OS, the proposed method can use a subset of the data to update theimage.Unlike OS, the proposed method is convergent.In one helical CTreconstruction experiment, an implementation of the proposed algorithm usingone GPU converges more quickly than a state-of-the-art algorithm convergesusing four GPUs.Using four GPUs, the proposed algorithm reaches nearconvergence of a wide-cone axial reconstruction problem with over 220 millionvoxels in only 11 minutes.
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X-ray CT Image Reconstruction on Highly-Parallel Architectures.