A two-step Hilbert transform method for 2D image reconstruction

By Frédéric Noo, Rolf Clackdoyle, Jed D. Pack. Physics in Medicine and Biology, 2004

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Truncated Hilbert transform and image reconstruction from limited tomographic data (2006, methodology): “This remarkable relation leads to the following sufficient condition for exact and stable ROI reconstruction from 2D limited data [7]: The function μ can be reconstructed at a point r0 if one can find a unit vector n = (−sin φ0, cos φ0) and a simply connected segment Lμ ⊂ L of the line L parallel to”
Multiscale X-ray tomography of cementitious materials: A review (2020, neutral): “Typical reconstruction techniques are sinogram extrapolation [75, 76], differential backprojection [77, 78], total variation minimization [79–81] or regularization with other”
Compressed Sensing Based Interior Tomography (2009, methodology): “Hence, over the past few years a number of image reconstruction algorithms have been developed that use increasingly less raw data (Parker 1982, Noo et al 2004, Defrise et al 2006).”