Tomography

Basics

• What is an inverse problem?
• What is tomography^{tomography, sectional imaging}?
• What is a phantom?
• What is a sinogram?
• Lines determined by polar coordinates

Radon Transform and Computed Tomography

• Principles of CT (Computed Tomography)
• Radon Transform $\mathcal{R}$
  • Generalization: $n$-dimensional Radon Transform
  • Basic Properties
  • Radon Transform and Convolution
  • Radon Transform and Differentiation
• Back Projection $\mathcal{R}^{\#}$: The Dual of Radon Transform
• Fourier Slice Theorem
• Inverse Radon Transform
• Hilbert Transform

Cone-beam Radon Transform

• Principles of the Compton Camera

Photoacoustic Tomography (PAT)

• Principles of PAT (Photoacoustic Tomography)

Magnetic Resonance Imaging (MRI)

• What is Magnetic Resonance Imaging?
• Principles of Magnetic Resonance Imaging

Simulation

• Using the Shepp-Logan phantom in Julia, MATLAB, Python
• Using the Radon Transform in Julia, MATLAB, Python
• How to use back projection in Julia back_projection()
• How to use inverse Radon transform in Julia iradon()

Medical Imaging

• Structural and Functional Medical Imaging
• Types of Medical Imaging Cross-sections
• [Medical Imaging File Extensions]