CS 473 | SCS

The objective of this course is to provide students with an overview of the computational and mathematical methods in medical image processing. The course covers the main sources of medical imaging data (CT, MRI, PET, and ultrasound). We will study many of the current methods used to enhance and extract useful information from medical images. A variety of radiological diagnostic scenarios will be used as examples to motivate the methods.

Intended Audience

Students interested in medical imaging, as well as health and medicine, will find this course useful. The course has some crossover with other fields of image and signal processing, and students interested in remote sensing and computer graphics might also find this course helpful.

Related Courses

Prerequisites: AMATH 242/341/CM 271/CS 371 or CS 370. Not open to General Mathematics students

Hardware/Software

References

Schedule

Outline

Resampling (5 hours)

Will briefly cover sampling theory, and a variety of interpolation methods, including nearest-neighbour, linear, cubic & higher-order, and Fourier (using the FFT). Use these methods to implement spatial image transformations (rigid and non-rigid).

Sources of Medical Images (10 hours)

Briefly discuss the physics of X-ray, CT, PET, MRI, and ultrasound. Reconstruction techniques for CT (filtered back projection) and MRI (using the FFT). Will also include a section on the theory of the Radon transform, the Fourier transform, and how they relate to each other.

Image Enhancement (4 hours)

Contrast adjustment, denoising (convolution, FFT), deblurring (solving an ill-conditioned sparse linear system), edge detection (numerical approximation to a partial derivative), anisotropic diffusion (numerical solution of partial differential equations), super-resolution.

Registration (motion correction) (8 hours)

We will study intensity-based methods, including a variety of cost functions (correlation, least squares, mutual information, robust estimators), and optimization techniques (fixed-point iteration, gradient descent, Nelder-Mead simplex method, etc.). Implement registration for rigid and non-rigid transformations. MRI motion compensation.

Segmentation (tissue classification) (7 hours)

Discuss simple methods such as thresholding, region growing and watershed. More depth on the method of snakes (adaptive mesh), level set method (numerical solution of partial differential equations), and clustering (classifiers).

Functional MRI (optional) (3 hours)

Briefly overview FMRI experiments. Use linear regression analysis to find active brain regions. Linear least squares (QR factorization). Effects of physiological motion (cardiac and respiratory motion).