Iterative CBCT reconstruction using Hessian penalty

Tao Sun, Nanbo Sun, Jing Wang, Shan Tan

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Statistical iterative reconstruction algorithms have shown potential to improve cone-beam CT (CBCT) image quality. Most iterative reconstruction algorithms utilize prior knowledge as a penalty term in the objective function. The penalty term greatly affects the performance of a reconstruction algorithm. The total variation (TV) penalty has demonstrated great ability in suppressing noise and improving image quality. However, calculated from the first-order derivatives, the TV penalty leads to the well-known staircase effect, which sometimes makes the reconstructed images oversharpen and unnatural. In this study, we proposed to use a second-order derivative penalty that involves the Frobenius norm of the Hessian matrix of an image for CBCT reconstruction. The second-order penalty retains some of the most favorable properties of the TV penalty like convexity, homogeneity, and rotation and translation invariance, and has a better ability in preserving the structures of gradual transition in the reconstructed images. An effective algorithm was developed to minimize the objective function with the majorization-minimization (MM) approach. The experiments on a digital phantom and two physical phantoms demonstrated the priority of the proposed penalty, particularly in suppressing the staircase effect of the TV penalty.

Original languageEnglish (US)
Pages (from-to)1965-1987
Number of pages23
JournalPhysics in medicine and biology
Issue number5
StatePublished - Feb 21 2015


  • Hessian regularization
  • cone-beam CT
  • iterative reconstruction
  • majorizationminimization approach
  • total variation penalty

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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