Lambda tomography (LT) is to reconstruct a gradient-like image ofan object only from local projection data. It is potentially animportant technology for medical X-ray computed tomography (CT) ata reduced radiation dose. In this paper, we prove the firstgeneral formula for exact and efficient fan-beam LT from datacollected along any smooth curve based on even and odd dataextensions. As a result, an LT image can be reconstructed withoutinvolving any data extension. This implies that structures outsidea scanning trajectory do not affect the exact reconstruction ofpoints inside the trajectory even if the data may be measuredthrough the outside features. The algorithm is simulated in acollinear coordinate system. The results support our theoreticalanalysis.
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