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UBC Theses and Dissertations

Sparsity-based methods for image reconstruction and processing in cone-beam computed tomography Karimi, Davood


X-ray computed tomography (CT) is an essential tool in modern medicine. As the scale and diversity of the medical applications of CT continue to increase, the quest for reducing the radiation dose becomes of extreme importance. However, producing high-quality images from low-dose scans has proven to be a serious challenge. Therefore, further research in developing more effective image reconstruction and processing algorithms for CT is necessary. This dissertation explores the potential of patch-based image models and total variation (TV) regularization for improving the quality of low-dose CT images. It proposes novel algorithms for 1) denoising and interpolation of CT projection measurements (known as the sinogram), 2) denoising and restoration of reconstructed CT images, and 3) iterative CT image reconstruction. For sinogram denoising, patch-based and TV-based algorithms are proposed. For interpolation of undersampled projections, an algorithm based on both patch-based and TV-based image models is proposed. Experiments show that the proposed algorithms substantially improve the quality of CT images reconstructed from low-dose scans and achieve state-of-the-art results in sinogram denoising and interpolation. To suppress streak artifacts in CT images reconstructed from low-dose scans, an algorithm based on sparse representation in coupled learned dictionaries is proposed. Moreover, a structured dictionary is proposed for denoising and restoration of reconstructed CT images. These algorithms significantly improve the image quality and prove that highly effective CT post-processing algorithms can be devised with the help of learned overcomplete dictionaries. This dissertation also proposes two iterative reconstruction algorithms that are based on variance-reduced stochastic gradient descent. One algorithm employs TV regularization only and proposes a stochastic-deterministic approach for image recovery. The other obtains better results by using both TV and patch-based regularizations. Both algorithms achieve convergence behavior and reconstruction results that are better than widely used iterative reconstruction algorithms compared to. Our results show that variance-reduced stochastic gradient descent algorithms can form the basis of very efficient iterative CT reconstruction algorithms. This dissertation shows that sparsity-based methods, especially patch-based methods, have a great potential in improving the image quality in low-dose CT. Therefore, these methods can play a key role in the future success of CT.

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