PHYM434 Imaging and Signal Processing

2007-2008

Aims

Personal computers are now powerful enough to perform sophisticated image-processing and, as a result, techniques that a few years ago required 'super-computers' are being routinely applied to new areas of science and engineering. In this module, students will learn how a time varying signal is processed to form a two- or three-dimensional image, and how such images are manipulated and used to encode information. Examples are drawn from medical imaging, with particular emphasis on the physics of magnetic resonance imaging (MRI).

Intended Learning Outcomes

A student should be able to:

Module Specific Skills

• describe the operation of a range of signal-processing systems;
• analyse signal-processing operations, particularly in terms of the correspondence between operations in the time (space) domain and operations in the Fourier, Laplace or z domain;
• explain the generation of a free-induction decay and gradient and spin echoes and their subsequent utilisation for magnetic resonance imaging;
• use Fourier techniques for image generation;
• describe the basic principles of x-ray computed tomography;

Discipline Specific Skills

• apply the concepts of convolution and deconvolution to the solution of problems;
• apply the concept of k-space to the solution of problems;
• outline the possibilities offered by complex digital hardware, including image processing.

Personal and Key Skills

• undertake co-operative learning though peer-group discussions.

Learning and Teaching Methods

Lectures and group discussions (20×1hr), directed reading, problems classes (2×1hr).

Assignments

Students are encouraged to tackle questions related to a particular part of the module and these are marked by the lecturer and discussed with the students.

Assessment

One 90-minute examination (100%).

Syllabus Plan and Content

1. Signal processing
   1. Basic concepts in 1D: transfer function, amplitude response, phase response; filters;
   2. A-to-D conversion and aliasing
   3. Anti-aliasing filters and the Gibbs phenomenon
   4. Signal-averaging techniques to retrieve signals from noise
2. Transforms and their applications
   1. 1D Fourier, Laplace and z-transform
   2. Digital filters: example of transversal filter
   3. FFT analysis and windowing
   4. Convolution and deconvolution
   5. Extensions to 2D and 3D
3. Images and image processing
   1. Effect of pixel size and number of grey levels
   2. Spatial filtering: edge detection, smoothing, point spread function, modulation transfer function
4. X-ray computed tomography
   1. Outline of the imaging system
   2. image processing: back projection and filtered back projection
5. Basic Concepts in Nuclear Magnetic Resonance
   1. Hydrogen atom - magnetic moment, Larmor frequency
   2. Classical and quantum mechanical approach
   3. Boltzmann distribution, equilibrium magnetization
6. Bloch equations
   1. Pulsed and continuous-wave nuclear magnetic resonance
   2. Rotating frame
   3. Free induction decay, Fourier-transform properties
   4. Spin-lattice (T1) and spin-spin (T2) relaxation times
7. Magnetic-Resonance Imaging
   1. k-space description of imaging
   2. Slice selection
   3. gradient and spin echoes
   4. echo-planar imaging

Core Text

Supplementary Text(s)

Formative Mechanisms

Students can monitor their understanding of the module by attempting previous examination questions. Their solutions can be discussed with the lecturers who will provide any necessary help.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.