Low-dose CBCT Reconstruction Using Hessian Schatten Penalties

Liang Liu, Xinxin Li, Kai Xiang, Jing Wang, Shan Tan

Research output: Contribution to journalArticle

7 Scopus citations


Cone-beam computed tomography (CBCT) has been widely used in radiation therapy. For accurate patient setup and treatment target localization, it is important to obtain high-quality reconstruction images. The total variation (TV) penalty has shown state-of-the-art performance in suppressing noise and preserving edges for statistical iterative image reconstruction, but it sometimes leads to the so-called staircase effect. In this study, we proposed to use a new family of penalties — the Hessian Schatten (HS) penalties — for CBCT reconstruction. Consisting of the second-order derivatives, the HS penalties are able to reflect the smooth intensity transitions of the underlying image without introducing the staircase effect. We discussed and compared the behaviors of several convex HS penalties with orders 1, 2, and + ∞ for CBCT reconstruction. We used the majorization-minimization approach with a primal-dual formulation for the corresponding optimization problem. Experiments on two digital phantoms and two physical phantoms demonstrated the proposed penalty family’s outstanding performance over TV in suppressing the staircase effect, and the HS penalty with order 1 had the best performance among the HS penalties tested.

Original languageEnglish (US)
JournalIEEE Transactions on Medical Imaging
StateAccepted/In press - Oct 23 2017


  • CBCT
  • Hessian Schatten penalty
  • Image edge detection
  • Image reconstruction
  • image reconstruction
  • Imaging
  • Linear programming
  • Minimization
  • staircase effect
  • Three-dimensional displays
  • TV
  • TV

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

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