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Modern tomographic imaging techniques such as computed tomography (CT) and magnetic resonance imaging (MRI) have been used widely for non-invasively acquiring information within the subjects under study. In the last few years, there have been significant advances in tomographic imaging methods. In this presentation, author will discuss some of the recent algorithm developments for obtaining tomographic images of practical utility from data that are considered otherwise highly incomplete from the perspective of the conventional imaging theory. Emphasis will be placed on discussion of some newly developed ideas and algorithms for effective image reconstruction from highly sparse data in CT and MRI. These advances may allow opportunities for devising innovative tomographic imaging applications of highly significant practical merit in biomedical, industrial, security, and other fields. Various examples involving real, challenging CT and MRI imaging data will be used to illustrate and validate these new developments.