While classic CT theory is for exact reconstruction of a whole cross-section or an entire object, real-world applications often focus on smaller regions of interest (ROIs). The long-standing “interior problem” is to reconstruct an internal ROI only from truncated projections associated with x-rays through the ROI. In 2007, mathematical analysis and numerical results were published demonstrating that the interior problem can be solved in an exact and stable fashion if a subregion in the ROI is known. Such knowledge of a subregion is often available in practice; for example, the x-ray linear attenuation coefficients of air, water, blood, or other calibrated structures. Even without exact subregion knowledge, it was recently shown that interior tomography could still be exactly performed via compressive sensing. In this presentation, I will discuss the principles and implications of interior tomography to minimize radiation dose, handle large objects, improve temporal resolution, and be extended into other imaging modalities such as MRI, SPECT and US.
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