Accurate image reconstruction within and beyond the field-of-view of CT system from data with truncation

Objective. Accurate image reconstruction from data with truncation in x-ray computed tomography (CT) remains a topic of research interest; and the works reported previously in the literature focus largely on reconstructing an image only within the scanning field-of-view (FOV). We develop algorithms to invert the truncated data model for numerically accurate image reconstruction within the subject support or a region slightly smaller than the subject support.Methods. We formulate image reconstruction from data with truncation as an optimization program, which includes hybrid constraints on region-based image total-variation (TV) and imageℓ1-norm (L1) for effectively suppressing truncation artifacts. An algorithm, referred to as the TV-L1 algorithm, is developed for image reconstruction (i.e. inversion of the data model) from data with truncation through solving the optimization program.Results. We perform numerical studies to evaluate accuracy and stability of the TV-L1 algorithm by using simulated and real CT data. Accurate images can be obtained stably by use of the TV-L1 algorithm within the subject support, or a region substantially larger than the FOV, from data with truncation of varying degrees.Conclusions. The TV-L1 algorithm can invert the truncated data model to accurately and stably reconstruct images within the subject support, or a region slightly smaller than the subject support but substantially larger than the FOV.Significance. Accurate image reconstruction within the subject support, or a region substantially larger than the FOV, from data with truncation can be of theoretical and practical implication. The insights and TV-L1 algorithm may also be generalized to accurate image reconstruction from data with truncation in other tomographic imaging modalities.