Recently, three new designs of CT scanners called low-dose CT, sparse-view CT, and interior CT are attracting much attention in CT community. Consequently, development of corresponding image reconstruction methods has become an area of active research. The low-dose CT refers to CT in which projection data is measured with low-dose irradiation, and the sparse-view CT refers to CT in which a number of measured projection data is reduced to decrease patient dose. This paper consists of the following two major parts. In the first part, we review fundamentals of statistical image reconstruction methods (also called as iterative reconstruction methods), which have been already incorporated into commercial CT scanners as reconstruction methods for low-dose imaging protocols. In the second part, we review fundamentals of compressed sensing including total variation regularization, which is attracting much attention as major tools to develop reconstruction methods for sparse-view CT.
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