Abstract: Many image processing problems, including noise removal, deblurring, and segmentation, can be formulated as optimization problems. This approach is very successful at producing high quality state-of-the-art results, where research at UCLA has made significant contributions. This talk will reveal the key steps to this methodology by walking through the Rudin-Osher-Fatemi noise removal model. I will also show from my own work an optimization-based method for image zooming. Live examples will be shown of several image processing problems.