Simultaneous estimation of attenuation and activity images using optimization transfer

Matthew Jacobson, Jeffrey A. Fessler

Research output: Contribution to conferencePaperpeer-review


This paper addresses the application of optimization transfer to simultaneous statistical estimation of attenuation and activity images in tomographic image reconstruction. Although the technique we propose has wider applicability, we focus on the problem of reconstructing from data acquired via a post-injection transmission scan protocol. In this protocol, emission scan data is supplemented with transmission scan data that is acquired after the patient has received the injection of radio-tracer. The negative loglikelihood function for this data is a complicated function of the activity and attenuation images, leading to an objective function for the model that is difficult to minimize for the purpose of estimation. Previous work on this problem showed that when either the attenuation or activity image was held fixed, a paraboloidal surrogate could be found for the negative loglikelihood as a function of the remaining variables. This led to an algorithm in which the model's objective function is alternately minimized as a function of the attenuation and activity, using the optimization transfer technique. In the work we present here, however, we develop bivariate surrogates for the loglikelihood, i.e., functions that serve as surrogates with respect to both the attenuation and activity variables. Hence, simultaneous minimization in all variables can be carried out, potentially leading to convergence in fewer surrogate minimizations.

Original languageEnglish (US)
Number of pages5
StatePublished - 2002
Event2001 IEEE Nuclear Science Symposium Conference Record - San Diego, CA, United States
Duration: Nov 4 2001Nov 10 2001


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


  • Bivariate
  • Optimization transfer
  • Post-injection
  • Surrogate

ASJC Scopus subject areas

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


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