Fourier and Nyquist

Question 1

Spatial Domain

Answer 1

• Image represented as counts/pixel in a matrix

Question 2

Frequency domain

Answer 2

• Image represented as group of low,
  middle, and high frequency wavelengths
• Plotted as frequency vs. amplitude or a
  collection of sine and cosine waves

Question 3

Fourier Transform

Answer 3

• a mathematical process whereby data is converted from the spatial domain to the spatial frequency domain
• expressed as a signal or an image as a series of sine waves with varying frequencies and amplitudes
• Frequency may be expressed as:
• cycles/cm (cm-1)
• cycles/mm (mm-1)
• cycles/pixel
• a fraction of the Nyquist frequency

Question 4

Why convert to the frequency domain?

Answer 4

• noise and background filtering

Question 5

Nyquist frequency

Answer 5

• The highest frequency that can ne represented by the imaging system
• determined by pixel size
• Nyquist frequency= 1/ (2 x pixel dimension in mm)

Question 6

Nyquist sampling theorem

Answer 6

• the maximum spatial frequency that we
  can observe is only half of the sampling
  frequency that we use to acquire the
  image
• visualization of a repeating cycle
  requires at least 2 pixels per cycle

Question 7

Sampling frequency equation

Answer 7

• sampling frequency= number of pixels/FOV

Question 8

Aliasing

Answer 8

• an artifact where higher frequency components of an image or signal are incorrectly interpreted at lower frequencies
• causes distortion of the image or signal
• occurs whe high frequencies beyond nyquist are used in 3D image reconstruciton