Course Outline


The course starts with an introduction to multidimensional Fourier transforms. It then goes into four different types of imaging systems. Each of these sections is two weeks. The first week is a description of the physics and geometry of a typical system that uses that imaging mechanism. The second week examines a specific signal processing problem that arises with that modality. Matlab experiments will involve implementing these algorithms on real and simulated data.


Section 0: Multidimensional Fourier Transforms

Week 1

  • Introduction to the course

  • Review of 1D Fourier transforms

  • Introduction to Multidimensional Fourier Transforms

Week 2

  • 2D and 3D Fourier Transforms

  • Sampling in multiple dimensions

Section 1: Projection Imaging Systems

Week 3

  • Physics and geometry of projection X-Ray imaging.

Week 4

  • Image quality metrics, SNR, CNR, impulse response, MTF, noise characteristics

  • Matlab: Measuring SNR, CNR, and MTF in numerical phantoms

Section 2: Backprojection Imaging Systems

Week 5

  • Physics and geometry of X-Ray CT

  • Description of PET and SPECT

Week 6

  • Backprojection reconstruction algorithms and geometries

  • Matlab: Implement either convolution backprojection, or Fourier interpolation reconstruction

Section 3: Beam Forming Imaging Systems

Week 7

  • Physics of ultrasound imaging systems

  • Common imaging geometries

Week 8

  • Beam forming with ultrasound transducer arrays

  • Dynamic focus on transmit and receive

  • Matlab: Implement dynamic focus on receive using ultrasound data.

Section 4: Fourier Encoding Systems

Week 9

  • Physics and geometry of MRI systems

Week 10

  • Reconstruction of MRI images

  • Either Fourier interpolation or reconstruction from partial data

  • Matlab: Implement partial k-space reconstruction using MR data