MATH 315 (Fall 2014)

Instructor: Dr. Thomas Hoft

Imaging, Inverse Problems, and Numerical Linear Algebra: In this course we’ll study mathematical models of imaging: how images are formed, how they are degraded by fundamental limitations, and (most importantly) how we can restore them to their original splendor. We’ll develop, analyze, and implement practical numerical methods for deblurring images in this mathematical framework. We’ll also dig into some numerical linear algebra that comes up along the way.

 

MATH 315 (Fall 2013)

Instructor: Dr. Pat Van Fleet

Discrete Wavelet Transformations and Their Applications: We will cover some of the newest mathematical ideas of the late 20th century in this course. We will begin with a discussion of block matrix arithmetic and from there learn about digital image basics. From this point, we will learn about a wavelet transformation that allows us to construction a rudimentary image compression algorithm. To develop a more advanced algorithm requires the development of more sophisticated wavelet transformations. This is where we will shift gears. After learning about Fourier series and convolution, we will develop the mathematics we need to study applications such as digital image compression, image edge detection, and signal de-noising. In particular, we will learn about the wavelet transformations that are used in the JPEG2000 image compression standard and the FBI fingerprint compression algorithm.

If you are a mathematics major and have always wondered how to really use mathematics in applications, here's your big chance. But be warned - this is NOT typically the way you've done mathematics in other courses. There is no "right way" to do many of these applications.  This is typically unnerving for most mathematics students. It'll be fun!