Medical Imaging Fundamentals

📋 Course Outline

1. Sampling model and aliasing
2. Nyquist theorem and anti-aliasing
3. Image quality measures
4. Contrast and modulation transfer function
5. Resolution and spread functions
6. Noise and random variables
7. Signal-to-noise ratio
8. Artifacts and distortions
9. Diagnostic accuracy metrics
10. ROC analysis

📖 1. Sampling model and aliasing

🔑 Key Concepts & Definitions

• Discrete sampled function : A discrete representation obtained by evaluating a continuous image at grid points spaced by sampling periods in each direction.
• Sampling periods : The spatial spacings 9x and 9y between neighboring sampled points along $x$ and $y$.
• Sampling frequencies : The quantities $1/\Delta x$ and $1/\Delta y$ that set how densely samples are taken along each axis.
• Aliasing : An under-sampling artefact where higher spatial frequency components appear as falsely lower frequencies in the sampled image.

📝 Essential Points

• In 2D rectangular sampling, the discrete image is $f_d(m,n)=f(m\Delta x,n\Delta y)$ for integers $m,n\ge 0$.
• Sampling too coarsely produces artefacts because the sampled representation cannot preserve the original frequency content.

💡 Memory Hook

Aliasing happens when “too few samples steal high frequencies and disguise them as low ones.”

📖 2. Nyquist theorem and anti-aliasing

🔑 Key Concepts & Definitions