Recovering missing slices of the discrete fourier transform using ghosts

Shekhar S. Chandra*, Imants D. Svalbe, Jeanpierre Guedon, Andrew M. Kingston, Nicolas Normand

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n\log-{2}n) (for an n=N\times N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.

    Original languageEnglish
    Article number6226457
    Pages (from-to)4431-4441
    Number of pages11
    JournalIEEE Transactions on Image Processing
    Volume21
    Issue number10
    DOIs
    Publication statusPublished - 2012

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