An analytic reconstruction method for limited-view tomography

Limited-view data are generated in many imaging applications, including positron emission mammography (PEM), x-ray tomosynthesis, and electron parametric resonance imaging (EPRI). In some imaging situations, certain views may be obstructed or impractical to imaging. It is well-known that limited-view data of an image function do not contain complete information for achieving exact reconstruction of the image function. When applying the conventional filtered backprojection (FBP) and assuming the measurements in the missing views are zeros, substantial image artifacts can be generated. As a result, approximate reconstructions of limited-view data are often achieved by using backprojection. Although this approach is incorrect, the results obtained can often reveal qualitative characteristics of the underlying image function that are useful in certain applications. Alternatively, iterative methods can be used to generate more accurate results, especially when a priori information is employed for regularizing the artifact-generating effects of the missing data. In both cases, theoretical prediction of the relationship between the obtained results and the underlying solutions are not available. Although exact reconstructions cannot be achieved, in this paper we will show that for an image function of compact support its limited-view projection data can be employed to estimate high-frequency components of a blurred solution. In addition, with a proper design only the zero-frequency (dc) components of the image row profiles cannot be estimated by the proposed method