A fixed point method for homotopic ℓ0-minimization with application to MR image recovery

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


A novel method for highly-undersampled Magnetic Resonance Image (MRI) reconstruction is presented. One of the principal challenges faced in clinical MR imaging is the fundamental linear relation between net exam duration and admissible spatial resolution. Increased scan duration diminishes patient comfort while increasing the risk of susceptibility to motion artifact and limits the ability to depict many physiological events at high temporal rates. With the recent development of Compressive Sampling theory, several authors have successfully demonstrated that clinical MR images possessing a sparse representation in some transform domain can be accurately reconstructed even when sampled at rates well below the Nyquist limit by casting the recovery as a convex ℓ1-minimization problem. While ℓ1-based techniques offer a sizeable advantage over Nyquist-limited methods, they nonetheless require a modest degree of over-sampling above the true theoretical minimum sampling rate in order to guarantee the achievability of exact reconstruction. In this work, we present a reconstruction model based on homotopic approximation of the ℓ0 quasi-norm and discuss the ability of this technique to reconstruct undersampled MR images at rates even lower than are achievable than with ℓ1-minimization and arbitrarily close to the true minimum sampling rate. A semi-implicit numerical solver is presented for efficient numerical computation of the reconstruction process and several examples depicting the capability for accurate MRI reconstructions from highly-undersampled K-space data are presented.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2008 - Physics of Medical Imaging
StatePublished - 2008
EventMedical Imaging 2008 - Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 18 2008Feb 21 2008

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2008 - Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA


  • ALG
  • OT

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


Dive into the research topics of 'A fixed point method for homotopic ℓ0-minimization with application to MR image recovery'. Together they form a unique fingerprint.

Cite this