42-431 (18-496)
Introduction to Biomedical Imaging and Image Analysis

Description: The aim of this course is to prepare upper level undergraduates so that they can be productive when faced with technical problems related to biomedical imaging. The basic underlying techniques (mathematics, physics, signal processing, data analysis) for understanding the several phenomena related to image formation in biomedical devices are presented. Several methods for computational information extraction from image data are also presented (segmentation, registration, pattern recognition, etc.). Course work will include homework assignments (including analytical and programming exercises) as well as an independent project. Field trips to observe biomedical imaging devices in action are also planned.

Prerequisite: 18-396 Signals and Systems (or 18-290) or permission of the instructor, working knowledge of Matlab, and some image processing experience.

Instructor: Gustavo K. Rohde, HH C 122, gustavor@cmu.edu.

Office hours: Wednesdays, 1-2:20pm, HHC 122.

Grading:

  • 60% Homework
  • 30% Project
  • 10% Class participation

Lectures:

Signal/image processing and data analysis
Background reading: Overview of signal processing (chapter 2 of Vetterli, Kovacevic pdf) , B-spline image processing pdf .

  • Linear algebra, vector spaces ( slides )
  • Introduction to Fourier Analysis ( slides )
  • Elements of signal processing (sampling, aliasing, reconstruction, interpolation) ( slides )
  • Image processing using B-splines
  • Multiresolution

System's view of biomedical imaging modalities
Background reading: Fluorescence microscopy ( pdf ), Magnetic Resonance Imaging ( web ), Computed Tomography ( pdf )

  • Microscopy (Light through an aperture, PSF, photon detection, fluorescence, widefield, confocal) ( slides I , slides II , slides III )
  • MRI (Bloch equations, precession, FID, frequency encoding, phase encoding) ( slides )
  • X-ray computed tomography (Fourier slice theorem, filtered back projection, modern approaches) ( slides )

Computational image analysis
Background reading: restoration (deconvolution, denoising) pdf , image registration pdf , image segmentation pdf

  • Linear inverse problems (Wiener filtering, Richardson-Lucy deconvolution, constrained least squares, etc) ( slides )
  • Image registration (point-based, intensity-based, rigid body, affine, nonrigid) ( slides I, slides II )
  • Image segmentation (thresholding, binary morphology, watershed, active contours, level set methods, etc.) ( slides )

Homework assigments:

Projects: