Image-reconstruction algorithms implemented on existing computerized tomography (CT) scanners require the collection of line integrals that are evenly spaced over 360 deg. In many practical situations, some of the line integrals are inaccurately measured or are not measured at all. In these limited-data situations, conventional algorithms produce images with severe streak artifacts. Recently, several other image-reconstruction algorithms were suggested, each tailored to a specific type of limited-data problem. These algorithms make minimal use of a priori knowledge about the image; only one has been demonstrated with real x-ray data. We present a new operator framework that treats all types of limited-data image-reconstruction problems in a unified way. From this framework we derive iterative convolution backprojection algorithms that make no restrictions on the location of missing line integrals. All available a priori information is incorporated by constraint operators. The algorithm has been implemented on a commercial CT scanner. We present examples of images reconstructed from real x-ray data in two limited-data situations and demonstrate the use of additional a priori information to reduce streak artifacts further.
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