For my first project of applied math, I used spectral filtering of noisy, simulated ultrasound images to locate a marble swallowed by a dog.  I analyzed a series of 20 three dimensional images of the dog’s digestive system with 64x64x64 voxels.  In order to remove noise, I first averaged all 20 images in the frequency domain to locate a peak frequency profile, and then spectrally filtered each of the images in the frequency domain, using a gaussian filter around the peak frequency profile.  I was able to locate the marble as a peak within each of the 20 filtered images.

The full paper describing this project is here.