Least squares framework for projection MRI reconstruction

Jens Gregor, F. R. Rannou

Research output: Contribution to journalConference article

4 Citations (Scopus)

Abstract

Magnetic resonance signals that have very short relaxation times are conveniently sampled in a spherical fashion. We derive a least squares framework for reconstructing three-dimensional source distribution images from such data. Using a finite-series approach, the image is represented as a weighted sum of translated Kaiser-Bessel window functions. The Radon transform thereof establishes the connection with the projection data that one can obtain from the radial sampling trajectories. The resulting linear system of equations is sparse, but quite large. To reduce the size of the problem, we introduce focus of attention. Based on the theory of support functions, this data-driven preprocessing scheme eliminates equations and unknowns that merely represent the background. The image reconstruction and the focus of attention both require a least squares solution to be computed. We describe a projected gradient approach that facilitates a non-negativity constrained version of the powerful LSQR algorithm. In order to ensure reasonable execution times, the least squares computation can be distributed across a network of PCs and/or workstations. We discuss how to effectively parallelize the NN-LSQR algorithm. We close by presenting results from experimental work that addresses both computational issues and image quality using a mathematical phantom.

Original languageEnglish (US)
Pages (from-to)888-898
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4322
Issue number2
DOIs
StatePublished - Jan 1 2001
EventMedical Imaging 2001 Image Processing - San Diego, CA, United States
Duration: Feb 19 2001Feb 22 2001

Fingerprint

Magnetic resonance imaging
Least Squares
projection
Projection
Projected Gradient
Radon
Support Function
Least-squares Solution
Magnetic Resonance
Radon Transform
Nonnegativity
Linear system of equations
Friedrich Wilhelm Bessel
Image Reconstruction
Magnetic resonance
Phantom
Weighted Sums
Image reconstruction
Data-driven
Relaxation Time

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Least squares framework for projection MRI reconstruction. / Gregor, Jens; Rannou, F. R.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 4322, No. 2, 01.01.2001, p. 888-898.

Research output: Contribution to journalConference article

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