Today's Focus

• Briefly review and re-inforce imaging concepts.

• Finish up concept of spectroscopic imaging.

• Start in on Fourier transform concepts

• Fourier transform concepts aren't just important to MRI. Come across similar effects in lots of fields.
  • vibrational analysis of mechanical parts
  • other imaging modalities use reconstruction methods that have characteristic artifacts
  • use Fourier transform to analyze sound
  • use Fourier transform to locate junk in data in lots of fields
  • use Fourier transform to analyze images for many applications

• When doing the Fourier transform practical considerations make it impossible to perform continuous Fourier transform. Therefore, all results are approximations with observable artifacts.
  • Can't sample forever, so data is truncated
  • Data is generally sampled, don't have continuous functions
  • Know that signal is changing in time due to relaxation, so spin density is effectively multiplied by another function

• For the next two lectures, we are going to go over Fourier transform properties, how they impact MRI, but the principles are universal.