Peihua Qiu

         Jump Regression Analysis and Image Processing

Nonparametric regression analysis provides a statistical tool for estimating
regression curves or surfaces from noisy data. Conventional nonparametric
regression methods, however, are only appropriate for estimating continuous
regression functions. When a underlying regression function has jumps,
functions estimated by the conventional methods are not statistically consistent
at the jump positions. Recently, jump regression analysis (JRA) for estimating
jump regression functions is under rapid development, because JRA has broad
applications. One important application is image processing where a
monochrome image can be regarded as a surface of the image intensity
function which has jumps at the outlines of image objects. In this talk, I will
make a general introduction to the research area of JRA and some of its
applications in image processing. At the beginning of the talk, I will spend
several minutes to briefly describe some of my other research topics.