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Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets

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Abstract

This paper presents a novel method which reconstructs any desired 3D image resolution from raw cone-beam CT data. X-ray attenuation through the object is approximated using ridgelet basis functions which allow us to have multiresolution representation levels. Since the Radon data have preferential orientations by nature, a spherical wavelet transform is used to compute the ridgelet coefficients from the Radon shell data. The whole method uses the classical Grangeat’s relation for computing derivatives of the Radon data which are then integrated and projected to a spherical wavelet representation and back-reconstructed using a modified version of the well known back-projection algorithm. Unlike previous reconstruction methods, this proposal uses a multiscale representation of the Radon data and therefore allows fast display of low-resolution data level.

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Authors and Affiliations

  1. Bioingenium Research Group, Cra 30 No 45 03-Ciudad Universitaria, Facultad de Medicina, Universidad Nacional de Colombia, Bogotá DC, Colombia

    Francisco Gómez & Eduardo Romero

  2. Departamento de Física Matemática y Fluidos, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, 28080, Madrid, Spain

    Cristina Santa Marta

  3. Telemedicine Centre, National University of Colombia, Bogota, Colombia

    Eduardo Romero

Authors
  1. Francisco Gómez
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  2. Cristina Santa Marta
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  3. Eduardo Romero
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Correspondence to Eduardo Romero.

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Gómez, F., Santa Marta, C. & Romero, E. Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets. J Digit Imaging 24, 1087–1095 (2011). https://doi.org/10.1007/s10278-011-9369-y

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