A General Formula for Fan‐Beam Lambda Tomography

Lambda tomography (LT) is to reconstruct a gradient‐like image of an object only from local projection data. It is potentially an important technology for medical X‐ray computed tomography (CT) at a reduced radiation dose. In this paper, we prove the first general formula for exact and efficient fan‐beam LT from data collected along any smooth curve based on even and odd data extensions. As a result, an LT image can be reconstructed without involving any data extension. This implies that structures outside a scanning trajectory do not affect the exact reconstruction of points inside the trajectory even if the data may be measured through the outside features. The algorithm is simulated in a collinear coordinate system. The results support our theoretical analysis.