Applied/Numerical Linear Algebra-Suggestions for Project I am looking for suggestions for a research project in applied/numerical linear algebra. As far as requirements, there really aren't any except that the topic has to tie in somehow with numerical methods used to solve problems in linear algebra. One suggestion that popped up was "Singular Value Decomposition (SVD) and image processing". The text we are using is "Applied Numerical Linear Algebra" by James W. Demmel, and we are expected to understand the material at least at that level. Any suggestions are most welcome, thanks!
 A: Not sure if this will be too advanced, but there's the discrete Radon transform. The idea is basically: say you have a matrix of unknown numbers, you take as your data the sum along any row, column, or diagonal, and your goal is to recover the original numbers.
This paper by Beylkin should be understandable to someone with your background:
http://amath.colorado.edu/pub/wavelets/papers/BEYLKI-1987.pdf
A key tool in the inversion process is the fast Fourier transform (FFT) which is perhaps the most important numerical algorithm ever. The abstract notion of a Fourier transform is also very important to signal processing (and endless other branches of mathematics).
One application is to medical imaging / the CT scan: if the numbers are density of tissue inside someone's body, the sum along a line (row/column/etc.) corresponds to the attenuation of an x-ray passing through that tissue. Thus, by probing someone's body with x-rays, you map the density of the stuff inside them.
The continuous analog of this is the Radon transform / X-ray transform, and they require some heavier math, but I would still recommend reading about them as background.
