California State University - Stanislaus
Title: Calculus of Variations with an Application to Image Processing
- Jung-Ha An
Dates of Program: May 29 – July 6, 2012
An image is a matrix of pixels arranged in columns and rows. Image processing is any form of signal processing that refers to the process of computing with images. Since 1960s, it has been developed rapidly and became an important area in applied mathematics, computer science, and electrical engineering.
One major purpose of image processing is to make an image better by image sharpening and image restoration. The total variational model is widely used in image processing to obtain better images.
The proposed project has three purposes: a) to study and understand the total variational model in image processing; b) to learn how to obtain a minimal solution mathematically using calculus of variations, in particular Euler-Lagrange equations; c) to be familiar with various numerical schemes which approximate a minimal solution numerically including gradient descent method and finite difference schemes.
Student Researchers Supported by MAA:
- Paulos Alemu
- Joshua Galvez
- Jo Fawna Reali
- Susana Urquizo