| Todd Wittman, Department of Mathematics, The Citadel |
| Title: Enhancing Satellite Imagery using the Calculus of Variations |
| Abstract: Image processing is an interdisciplinary field that draws on various branches of mathematics including optimization, differential equations, and numerical analysis. I will discuss a mathematical approach to enhancing satellite imagery based on the calculus of variations. Satellite spectral images give more information about the objects in the scene, but this comes at the cost of reduced spatial resolution. To address this issue, we can fuse the spectral image with a high-resolution panchromatic image. This process is called pan-sharpening. Traditional pan-sharpening methods work well for low-dimensional multispectral datasets (4-6 bands), but do not extend to high-dimensional hyperspectral datasets (100-200 bands). We present a variational method that incorporates wavelets and Total Variation to sharpen hyperspectral images. Time permitting, we will discuss applications to density estimation. This is a joint work with Michael Moeller, Andrea Bertozzi, and Martin Burger. |