Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation

Rik Van De Walle, Harrison H. Barrett, Kyle J. Myers, Maria I. Altbach, Bart Desplanques, Arthur F. Gmitro, Ignace Lemahieu

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.

Original languageEnglish (US)
Pages (from-to)1160-1167
Number of pages8
JournalIEEE Transactions on Medical Imaging
Issue number12
StatePublished - 2000


  • Generalized reconstruction
  • Magnetic resonance imaging
  • Medical imaging
  • Pseudoinverse image reconstruction

ASJC Scopus subject areas

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


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