Basics: k-Space to Image Space
Holden H Wu1
1UCLA Radiology, Los Angeles, CA, United States

Synopsis

Keywords: Image acquisition: Reconstruction

MRI data acquisition and reconstruction are linked through the unique concept of “k-space.” This talk will begin with an overview of the MRI signal equation and essential mathematical methods. Next, this talk will introduce k-space and its key characteristics, and then proceed to cover MRI data sampling in k-space and basic MR image reconstruction from k-space data using the Fourier transform. Imaging considerations, such as artifacts due to undersampling, will also be discussed. Finally, this talk will summarize the important role of k-space in MRI and set the stage for advanced reconstruction methods that will be covered in subsequent talks.

Introduction

  • MR image acquisition and reconstruction
  • What is k-space?

MRI Signal Equation

  • Larmor equation
  • Signal localization using RF excitation
  • Gradient encoding of spatial information
  • MRI signal equation

Math Fundamentals

  • Complex numbers
  • Convolution
  • Fourier transform
  • Sampling theorem and Nyquist criteria

k-Space

  • MRI signal equation revisited
  • Fourier transform relationship between k-space and image space
  • Navigating in k-space using gradients
  • A closer look at spatial frequencies

Reconstructing MR Images from k-Space Data

  • Simple MRI pulse sequence
  • Image resolution and field-of-view
  • k-Space data sampling considerations
  • MRI scan time considerations
  • MRI signal equation and Fourier transform reconstruction
  • Examples

Imaging Considerations

  • Signal-to-noise ratio (SNR)
  • Undersampling artifacts: aliasing, Gibbs ringing

Summary and Outlook

  • What k-space represents
  • Basic MR image reconstruction
  • Advanced MR image reconstruction

Acknowledgements

Drs. Dwight Nishimura, John Pauly, Daniel Ennis, Peng Hu, and Kyung Sung.

References

No reference found.
Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)