An analytical SMASH procedure (ASP) for sensitivity-encoded MRI

Ray F. Lee, Charles R. Westgate, Robert G. Weiss, Paul A. Bottomley

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system. (C) 2000 Wiley-Liss, Inc.

Original languageEnglish (US)
Pages (from-to)716-725
Number of pages10
JournalMagnetic Resonance in Medicine
Issue number5
StatePublished - 2000
Externally publishedYes


  • ASP
  • Harmonics
  • Image reconstruction
  • Phase correction
  • Phase- encoding
  • Phased-arrays MRI

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


Dive into the research topics of 'An analytical SMASH procedure (ASP) for sensitivity-encoded MRI'. Together they form a unique fingerprint.

Cite this