Jump regression, image processing, and quality control

Images have been widely used in manufacturing applications for monitoring production processes, partly because they are often convenient and economic to acquire by different types of imaging devices. Medical imaging techniques, such as CT, PET, X-ray, ultrasound, magnetic resonance imaging (MRI), and functional MRI, have become a basic medical diagnosis tool nowadays. Satellite images are also commonly used for monitoring the changes of the earth's surface. In all these applications, image comparison and monitoring are the common and fundamentally important statistical problems that should be addressed properly. In computer science, applied mathematics, statistics and some other disciplines, there have been many image processing methods proposed. In this article, I will discuss (i) a powerful statistical tool, called jump regression analysis (JRA), for modeling and analyzing images and other types of data with jumps and other singularities involved, (ii) some image processing problems and methods that are potentially useful for image comparison and monitoring, and (iii) some of my personal perspectives about image comparison and monitoring.