Iterative projection onto convex sets for quantitative susceptibility mapping

Weiran Deng*, Fernando Boada, Benedikt A Poser, Claudiu Schirda, Victor Andrew Stenger

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


PURPOSE: Quantitative susceptibility map (QSM) reconstruction is ill posed due to the zero values on the "magic angle cone" that make the maps prone to streaking artifacts. We propose projection onto convex sets (POCS) in the method of steepest descent (SD) for QSM reconstruction.

METHODS: Two convex projections, an object-support projection in the image domain and a projection in k-space were used. QSM reconstruction using the proposed SD-POCS method was compared with SD and POCS alone as well as with truncated k-space division (TKD) for numerically simulated and 7 Tesla (T) human brain phase data.

RESULTS: The QSM reconstruction error from noise-free simulated phase data using SD-POCS is at least two orders of magnitude lower than using SD, POCS, or TKD and has reduced streaking artifacts. Using the l1 -TV reconstructed susceptibility as a gold standard for 7T in vivo imaging, SD-POCS showed better image quality comparing to SD, POCS, or TKD from visual inspection.

CONCLUSION: POCS is an alternative method for regularization that can be used in an iterative minimization method such as SD for QSM reconstruction.

Original languageEnglish
Pages (from-to)697-703
Number of pages7
JournalMagnetic Resonance in Medicine
Issue number2
Publication statusPublished - Feb 2015
Externally publishedYes


  • Algorithms
  • Brain
  • Humans
  • Image Enhancement
  • Image Interpretation, Computer-Assisted
  • Magnetic Resonance Imaging
  • Phantoms, Imaging
  • Reproducibility of Results
  • Sensitivity and Specificity

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