Image Processing (mentor: Dr. Hyeona Lim)
Images in our daily lives occur in many forms such as digital or analog pictures, scanned documents, satellite pictures, etc. Therefore, the improvement in quality of images becomes more and more important. The images generated by a picture digitization generally produce errors due to a mechanical imperfection or physics of picture acquisition. These errors can be detected, analyzed, and reduced by the methods of image processing such as noise removal, sharpening of edges, segmentation of images to isolate object regions, and deblurring. As the world requires higher levels of reliability and efficiency in images, mathematical image processing has become and important component to answer fundamental questions.
In this project, we will study image denoising and segmentation techniques based on the partial differential equation (PDE) model. The problems have applications to geological synthetic aperture radar (SAR) images and medical imagery. New models for speckle image denoising will be considered and studied both mathematically and computationally. We will also develop method of background subtraction as a pre-processing for other medical image segmentation techniques in order to minimize the difficulties of segmentation of unclear edges.