Two-Dimensional Imaging

Winter 2012-2013

 

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Course description:

"A picture is worth a thousand words" -- these days it is more likely that a picture will be represented by a thousand kilobytes, and viewed through a digital computer. In this course we will investigate how digital images are formed and manipulated, with emphasis on the theory and practice of digital implementation of mathematical models of imaging systems.

The course will consist of theoretical material describing the mathematics of images and imaging, as well as computer exercises designed to introduce methods of real-world data manipulation. Topics will include representation of two-dimensional data, impulse functions in two dimensions, the Fourier transform, convolution, sampling, interpolation, digital filtering, and techniques for imaging such as synthetic aperture radar and computed tomography, as well as applications for computerized image data. We will rely heavily on material available in the text, and relevant additional material will be handed out to you in class. We will also introduce some outside materials, mainly in the last third of the course, when we deal with applications of the mathematical tools developed initially. Lecture notes will be handed out routinely, and special handouts will also be distributed from time to time. Reading assignments will be given for most class meetings. These may be from the text or from other sources, most of which will be on reserve at Terman Engineering Library. Homework assignments will generally be given on Fridays and collected on Fridays, with the results handed back by the following Monday or Wednesday. Cooperation on homework is encouraged, but you are expected to keep the work on an approximately equal basis. There will be one midterm exam plus a final term project. Grades will be based on homework, the midterm exam, and the project, with weightings of approximately 40% on the final project, 25% on the midterm, 30% on homework, and up to 5% extra credit problems.

We will implement many of the concepts presented in the course in a series of computer exercises designed to acquaint you with computer manipulation of actual image data. The resources required for this should be within the capability of the class computer accounts in the Leland system, but you are free to implement them on any machine on which you are comfortable. You will be given access to the Image Systems Engineering Lab in the basement of Packard (room 021), which is set up with Linux computers connected to the Leland system through AFS. Most of the exercises can be done using matlab, although many examples will be given using C and Fortran language routines. Again, you are permitted to implement the exercises using any language or system you wish-- it is the result that counts.

A rough schedule of the course is as follows, with more details in the course syllabus following. We first introduce the ideas concerning how we define images and imaging. The next several weeks will cover how we apply systems theory, such as transforms and impulse functions, to two dimensional imaging systems. This will be accompanied by several computer implementation exercises designed to introduce you the the real world of data, where things are often not as tidy as they may be in more theoretical circumstances. Topics such as sampling and interpolation, important in all data manipulation, follow. After the midterm, we begin a series of illustrations of how the theoretical constructs from the first half of the course are applied in practice. We'll start with imaging the Earth's subsurface through seismic profiling, then address radio astronomy imaging techniques. Finally we discuss tomography and reconstruction from slices and also imaging radar techniques. Each of these will be accompanied by additional theoretical material for its particular geometry, and you will be expected to develop computer code that produces images using each technique. I will supply the data, you the image.

The final project will be a team effort consisting of the design and simulation of an actual imaging system to solve a real problem. You will be free to choose your own problem; several examples will be provided that you may use. Past problems students have developed include subsurface oil reservoir imaging, spaceborne radar systems, and a detector of extra-solar planets.

A course syllabus and a list of reference books are available through the menu at left. Assigned readings will usually be from the primary text. You may also find that a different book presents material in ways you can more easily understand, although the selected text is quite good.


Textbook info:
Bracewell, R.N., Fourier Analysis and Imaging, Kluwer, New York, 2003.

Prerequisites:
EE261, or equivalent familiarity with Fourier transforms. Programming experience, at least at the Matlab level, will be helpful for the homework. Some familiarity with linear systems and signal processing will also help.