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This paper proposes a spatial-Radon domain CT image reconstruction modelbased on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF modelcombines the idea of joint image and Radon domain inpainting model of\cite{Dong2013X} and that of the data-driven tight frames for image denoising\cite{cai2014data}. It is different from existing models in that both CT imageand its corresponding high quality projection image are reconstructedsimultaneously using sparsity priors by tight frames that are adaptivelylearned from the data to provide optimal sparse approximations. An alternativeminimization algorithm is designed to solve the proposed model which isnonsmooth and nonconvex. Convergence analysis of the algorithm is provided.Numerical experiments showed that the SRD-DDTF model is superior to the modelby \cite{Dong2013X} especially in recovering some subtle structures in theimages.

CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization