Theoretical study of penalized-likelihood image reconstruction for region of interest quantification

Jinyi Qi, Ronald H. Huesman

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Region of interest (ROI) quantification is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Statistical image reconstruction methods based on the penalized maximum-likelihood (PML) or maximum a posteriori principle have been developed for emission tomography to deal with the low signal-to-noise ratio of the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the regularization parameter in PML reconstruction controls the resolution and noise tradeoff and, hence, affects ROI quantification. In this paper, we theoretically analyze the performance of ROI quantification in PML reconstructions. Building on previous work, we derive simplified theoretical expressions for the bias, variance, and ensemble meansquared-error (EMSE) of the estimated total activity in an ROI that is surrounded by a uniform background. When the mean and covariance matrix of the activity inside the ROI are known, the theoretical expressions are readily computable and allow for fast evaluation of image quality for ROI quantification with different regularization parameters. The optimum regularization parameter can then be selected to minimize the EMSE. Computer simulations are conducted for small ROIs with variable uniform uptake. The results show that the theoretical predictions match the Monte Carlo results reasonably well.

Original languageEnglish (US)
Pages (from-to)640-648
Number of pages9
JournalIEEE Transactions on Medical Imaging
Issue number5
StatePublished - May 2006


  • Emission tomography
  • Image reconstruction
  • Maximum a posteriori
  • Parameter estimation
  • Penalized likelihood
  • Quantification

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics


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