Nonnegative definite quadratic penalty design for penalized-likelihood reconstruction

J. Webster Stayman, Jeffrey A. Fessler

Research output: Contribution to conferencePaperpeer-review

6 Scopus citations


Likelihood-based estimators with conventional regularization methods generally produces images with nonuniform and anisotropic spatial resolution properties. Previous work on penalty design for penalized-likelihood estimators has led to statistical reconstruction methods that yield approximately uniform "average" resolution. However some asymmetries in the local point-spread functions persist. Such anisotropies result in the elongation of otherwise symmetric features like circular lesions. All previously published penalty functions have used nonnegative values for the weighting coefficients between neighboring voxels. Such nonnegativity provides a sufficient (but not necessary) condition to ensure that the penalty function is convex, which in turn ensures that the objective function has a unique maximizer. This paper describes a novel method for penalty design that allows a subset of the weighting coefficients to take negative values, while still ensuring convexity of the penalty function. We demonstrate that penalties designed under these more flexible constraints yield local point-spread functions that are more isotropic than the previous penalty design methods for 2D PET image reconstruction.

Original languageEnglish (US)
Number of pages4
StatePublished - 2001
Externally publishedYes
Event2001 IEEE Nuclear Science Symposium Conference Record - San Diege, CA, United States
Duration: Nov 4 2001Nov 10 2001


Other2001 IEEE Nuclear Science Symposium Conference Record
Country/TerritoryUnited States
CitySan Diege, CA

ASJC Scopus subject areas

  • Radiation
  • Nuclear and High Energy Physics
  • Radiology Nuclear Medicine and imaging


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