A least squares quantization table method for direct reconstruction of MR images with non-Cartesian trajectory

Dong Liang, Edmund Y. Lam, George S K Fung

Research output: Contribution to journalArticle

Abstract

The direct Fourier transform method is a straightforward solution with high accuracy for reconstructing magnetic resonance (MR) images from nonuniformly sampled k-space data, given that the optimal density compensation function is selected and the underlying magnetic field is sufficiently uniform. The computation however is very time-consuming, making it impractical especially for large-size images. In this paper, the least squares quantization table (LSQT) method is proposed to accelerate the direct Fourier transform computation, similar to the recently proposed methods such as using look-up table (LUT) or equal-phase-line (EPL). With LSQT, all the image pixels are first classified into several groups where the Lloyd-Max quantization scheme is used to ensure the minimal classification error. The representative value of each group is stored in a small-size LSQT in advance to reduce the computational load. The pixels in the same group receive the same contribution, which is calculated only once for each group instead of for each pixel, resulting in the reduction of computation because the number of groups is far smaller than the number of pixels. Finally, each image pixel is mapped into the nearest group and its representative value is used to reconstruct the image. The experimental results show that the LSQT method requires far smaller memory size than the LUT method and fewer multiplication operations than the LUT and EPL methods. Moreover, the LSQT method can perform large-size reconstructions that achieve comparable or higher accuracy as compared to the EPL and gridding methods when the appropriate parameters are given. The inherent parallel structure also makes the LSQT method easily adaptable to a multiprocessor system.

Original languageEnglish (US)
Pages (from-to)141-150
Number of pages10
JournalJournal of Magnetic Resonance
Volume188
Issue number1
DOIs
StatePublished - Sep 2007
Externally publishedYes

Fingerprint

Magnetic resonance
Least-Squares Analysis
magnetic resonance
Magnetic Resonance Spectroscopy
Pixels
Trajectories
trajectories
pixels
Fourier transforms
Fourier Analysis
Magnetic fields
Data storage equipment
Magnetic Fields
multiplication
magnetic fields

Keywords

  • Image reconstruction
  • Least squares quantization table
  • Lloyd-Max quantization
  • Non-Cartesian trajectory
  • Nonuniform distribution

ASJC Scopus subject areas

  • Molecular Biology
  • Physical and Theoretical Chemistry
  • Spectroscopy
  • Radiology Nuclear Medicine and imaging
  • Condensed Matter Physics

Cite this

A least squares quantization table method for direct reconstruction of MR images with non-Cartesian trajectory. / Liang, Dong; Lam, Edmund Y.; Fung, George S K.

In: Journal of Magnetic Resonance, Vol. 188, No. 1, 09.2007, p. 141-150.

Research output: Contribution to journalArticle

Liang, Dong ; Lam, Edmund Y. ; Fung, George S K. / A least squares quantization table method for direct reconstruction of MR images with non-Cartesian trajectory. In: Journal of Magnetic Resonance. 2007 ; Vol. 188, No. 1. pp. 141-150.
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