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Interior tomography with continuous singular value decomposition.

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      Abstract

      The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known sub-region in the ROI. In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known sub-region. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior sub-region knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the POCS type interior reconstructions.

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      Author and article information

      Journal
      IEEE Trans Med Imaging
      IEEE transactions on medical imaging
      Institute of Electrical and Electronics Engineers (IEEE)
      1558-254X
      0278-0062
      Nov 2012
      : 31
      : 11
      22907966
      10.1109/TMI.2012.2213304
      3773972
      NIHMS509580

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