Image Reconstruction via Truncated Lambda Tomography

摘要

This paper investigates the feasibility of reconstructing a Computed Tomography (CT) image from truncated Lambda Tomography (LT), a gradient-like image of it's original. An LT image can be regarded as a convolution of the object image and the point spread function (PSF) of the Calderon operator. The PSF's infinite support provides the LT image infinite support; even the original CT image is of compact support. When the support of a truncated LT image fully covers the compact support of the corresponding CT image, we develop an extrapolation method to recover the CT image more precisely. When the support of the CT image fully covers the support of the truncated LT image, we design a template-based scheme to compensate the cupping effects and reconstruct a satisfactory image. Our algorithms are evaluated in numerical simulations and the results demonstrate the feasibilities of our methods. Our approaches provide a new way to reconstruct high-quality CT images.