Limited view angle tomographic image reconstruction via total variation minimization

Julia Velikina, Shuai Leng, Guang Hong Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

45 Scopus citations


In tomosynthesis, cone-beam projection data are acquired from a few of view angles, which are not sufficient for an exact reconstruction of an image object using state-of-the-art image reconstruction algorithms. In the case of parallel-beam projections, the well-known projection-slice theorem may be utilized to transform the parallel-beam projections into the Fourier space of an image object. Due to the limited range of view angles, the available projection data can only populate a portion of Fourier space. Moreover, the angular sampling rate of the populated portion of the Fourier space may not satisfy the Nyquist criterion. Thus, reconstructed images using direct Fourier inversion contain severe streaking and distortion artifacts. In this paper, we present a novel image reconstruction method via minimizing the total variation (TV) of the reconstructed image for limited view angle X-ray computed tomography. Specifically, the missing data points in Fourier space, due to either the limited range or undersampling of view angles, are iteratively filled using the following two constraint conditions: (1) the total variation of the reconstructed image is minimized and (2) reconstructed image maintains fidelity to the sampled data in the Fourier space. Using analytical phantoms, numerical simulations were conducted to validate the new image reconstruction method. Images are compared with two other image reconstruction methods in terms of image artifact level and noise properties. Numerical results demonstrated that the new image reconstruction algorithm is superior to direct Fourier inversion reconstruction algorithm and the projection onto convex sets (POCS) image reconstruction algorithm.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2007
Subtitle of host publicationPhysics of Medical Imaging
EditionPART 2
StatePublished - Oct 15 2007
EventMedical Imaging 2007: Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 18 2007Feb 22 2007

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
NumberPART 2
ISSN (Print)1605-7422


OtherMedical Imaging 2007: Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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