Directional sinogram inpainting for limited angle tomography

Robert Tovey*, Martin Benning, Christoph Brune, Marinus J. Lagerwerf, Sean M. Collins, Rowan K. Leary, Paul A. Midgley, Carola Bibiane Schönlieb

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    24 Citations (Scopus)
    105 Downloads (Pure)


    In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of tomography, e.g. electron microscopy and mammography, physical limitations on acquisition lead to regions of data which cannot be sampled. Depending on the severity of the restriction, reconstructions can contain severe, characteristic, artefacts. Our model aims to address these artefacts by inpainting the missing data simultaneously with the reconstruction. Numerically, this problem naturally evolves to require the minimisation of a non-convex and non-smooth functional so we review recent work in this topic and extend results to fit an alternating (block) descent framework. We perform numerical experiments on two synthetic datasets and one electron microscopy dataset. Our results show consistently that the joint inpainting and reconstruction framework can recover cleaner and more accurate structural information than the current state of the art methods.

    Original languageEnglish
    Article number024004
    Number of pages29
    JournalInverse problems
    Issue number2
    Publication statusPublished - 1 Feb 2019


    • Anisotropy
    • Inpainting
    • Limited angle tomography
    • Nonconvex
    • Optimization
    • Tomography
    • Variational


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