The investigator and his colleaques study modeling and computational questions that arise in applying variational and partial differential equation methods to problems of image processing, and they develop effective new algorithms. These problems are computationally intensive and accurate and efficient methods are needed. They consider dual methods for image restoration by total variation, blind deconvolution of multi-channel images, ENO-wavelet compression of images with sharp edges, reduced Mumford-Shah models and multi-channel extensions for image restoration and segmentation, and new active contour models without edge-stopping. Topics of study include image restoration, compression, multispectral images, segmentation, and active contours. Applications in medical and chemical imaging, astronomical imaging, and multispectral automatic target recognition are pursued.
Image processing arises across engineering disciplines and the physical and medical sciences. Applications in the medical sciences and biotechnology field range from computer tomography to processing of microscopic images of molecular structures. In the enviromental area, satellite imaging has been used to map natural resources as well as enviromental pollution. In the area of manufacturing, imaging systems are used to detect defects automatically. In all of these applications, a key process is that of image restoration, namely, cleaning up an image polluted by noise and blurring. This is a central subject of this project. These problems are very computationally intensive due to the large number of pixels and the possibility of sequences of images (e.g. videos). Solving them requires clever mathematical algorithms as well as high performance computers. Beyond this, in the current revolution in commmunication and the use of the information highway, more images are being transmitted and better mathematical algorithms are needed to compress and remove noise and other distortions occuring in the transmission.
