Mentoring through Critical Transistion Points (MCTP)
Summer programs: 2013
Pre-REU Program: Signal and Image Analysis
As technology becomes more sophisticated, the need for efficiently handling vast amounts of data has grown tremendously. For example, a stroke victim might go to the emergency room at 3:00 in the morning. A CT scan is performed to assess the proper course of treatment, but no radiologist is readily available to read the results of the scan. What is happening more and more is that hospitals send out the data to another part of the world where an expert is readily available to interpret the scan. Naturally, it is desirable to transmit the data as efficiently as possible. There are two main obstacles to this:
- The data is sent via satellite or over a telephone line and the bandwidth available for transmission is limited.
- For various uncontrollable reasons, transmission introduces random errors or noise into the signal.
Thus it is important to compress the data without losing too much information as well as eliminate any noise in the received signal.
Other real-world examples where these obstacles arise abound: transmission to Earth of images and data from the mars lander or an interplanetary satellite, telephone calls, accessing FBI fingerprint files and surfing the web, to name a few. An example closer to home is the well-known fact that a compact disc can hold many more audio files in .mp3 format than in the usual cd format on an audio disc purchased at a store. There are two main tools used to analyze signals and images:
- Fourier analysis---good for time-independent wavelike features. For instance, one would want to filter out the crowd noise in a recording of a concert.
- Wavelets---good for isolated or local events such as eliminating a ``pop'' in an audio file.
In this program, the basic ideas behind the use of Fourier analysis and wavelets in signal and image analysis will be introduced. The material will be appropriate for students who have completed a typical three semester calculus sequence. Initially, in the morning sessions, a faculty member will present ideas, techniques and examples. For the afternoon sessions, faculty and graduate students will be available to provide further guidance to the students while they work on problems over the material presented in the morning sessions. As time goes on, the students will break up into groups and work on projects involving real-world examples.
Periodically there will be guest lectures by various faculty members on relevant contemporary topics. At the end of the program, the groups will present the results of their projects at a symposium in conjunction with our REU programs.
Minimum prerequistes are at least two semesters of college calculus including at least two courses in mathematics studied at an institution of higher learning. All students must be at least 18 years old at the start of the program.