Wavelet encoded MR image reconstruction with compressed sensing

Zheng Liu, Brian Nutter, Jingqi Ao, Sunanda Mitra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Traditional MRI scanners acquire samples of the encoded image in a spatial frequency (Fourier) domain, known as k-space. The recently developed theory of Compressed Sensing (CS) has shown that a natural image could be acquired and reconstructed from a reduced number of linear projection measurements at sub-Nyquist sample rates. CS is well suited to fast acquisition of MRI by sparse encoding in k-space. However, the commonly used Fourier-encoding MRI scheme only weakly satisfies the incoherent measurements constraint required for CS. MR images can be reconstructed from a more sparse wavelet-encoded k-space than from Fourier-encoded k-space with the same resolution. Wavelet-encoded MRI is flexible in spatially-selective excitations to yield an encoding scheme similar to the "universal encoding". In this work, a CS-MRI scheme has been investigated to accurately reconstruct MR images from sparsely wavelet-encoded k-space. This sparse encoding is achieved with tailored spatially-selective RF pulses, which are designed with Battle-Lemarie wavelet functions. The Fourier transforms of the Battle-Lemarie wavelet functions used as RF pulse profiles are smooth and decay rapidly to zero. This technique provides short RF pulses with relatively precise spatial excitation profiles. Simulator results show that the proposed encoding scheme has different characteristics than conventional Fourier and wavelet encoding methods, and this scheme could be applied to fast MR image acquisition at relatively high resolution.

Original languageEnglish
Title of host publicationMedical Imaging 2011
Subtitle of host publicationPhysics of Medical Imaging
StatePublished - 2011
EventMedical Imaging 2011: Physics of Medical Imaging - Lake Buena Vista, FL, United States
Duration: Feb 13 2011Feb 17 2011

Publication series

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


ConferenceMedical Imaging 2011: Physics of Medical Imaging
Country/TerritoryUnited States
CityLake Buena Vista, FL


  • Battle-Lemarie wavelet encoding
  • RF pulses
  • compressed sensing
  • fast MRI
  • sparse k-space


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