Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT

Alex Sawatzky, Qiaofeng Xu, Carsten O. Schirra, Mark A. Anastasio

Research output: Contribution to journalArticlepeer-review


The development of spectral X-ray computed tomography (CT) using binned photon-counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with K-edge materials. A practical issue in implementing this technique is the mitigation of the high-noise levels often present in material-decomposed sinogram data. In this work, the spectral X-ray CT reconstruction problem is formulated within a multi-channel (MC) framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality. Specifically, a MC penalized weighted least squares (PWLS) estimator is formulated in which the data fidelity term is weighted by the MC covariance matrix and sparsity-promoting penalties are employed. This allows the use of any number of basis materials and is therefore applicable to photon-counting systems and K-edge imaging. To overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight, a proximal variant of the alternating direction method of multipliers is employed to minimize the MC PWLS objective function. Computer-simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method.

Original languageEnglish (US)
Article number6808543
Pages (from-to)1637-1668
Number of pages32
JournalIEEE Transactions on Medical Imaging
Issue number8
StatePublished - Aug 2014
Externally publishedYes


  • Energy-resolved X-ray computed tomography (CT)
  • K-edge imaging
  • material-decomposition
  • multi-channel image reconstruction
  • sparsity-promoting regularization
  • statistical image reconstruction
  • total variation regularization

ASJC Scopus subject areas

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


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