A major obstacle in computed tomography (CT) is the reduction of harmful x-ray dosewhile maintainingthe quality of reconstructed images.Methods which exploit the sparserepresentations of tomographic images have long been known to improve the quality of reconstructions from low-dose data. Recent work has shown the promise of adaptive, ratherthan fixed, sparse representations.In particular, the synthesis dictionary learningframework has been shown to outperform traditional regularization techniques.However,these methods scale poorly with data size, and may be prohibitively expensive forpractical tomographic reconstruction.In this thesis, we propose a new method for image reconstruction from low-dose data.Themethod combines a statistical iterative reconstruction framework with an adaptivesparsifying transform penalty.An alternating minimization approach is used to jointlyreconstruct the image while learning a sparsifying transform adapted to the particularimage being reconstructed.The Alternating Direction Method of Multipliers is used toprovide a computationally efficient solution to the statistically weighted minimizationproblem.Numerical experiments are performed on phantom data and clinical CT images. Dose reductionis achieved through reduction in the number of views and reduction in the photon flux.The results indicate the adaptive sparsifying transform regularization outperformsstate-of-the-art synthesis sparsity methods at speeds rivaling total-variationregularization.
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Tomographic reconstruction with adaptive sparsifying transforms
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