Image processing is an interdisciplinary field at the intersection of science and engineering. Mathematical modeling of image signals not only supports various engineering applications in our daily lives (e.g., digital cameras, high-definition TV, ultrasound diagnosis and so on) but also offers a computational approach to understand sensory coding as a strategy for information processing in visual cortex. An improved understanding of image models is likely to lead to artifact-free signal processing systems that well match the perception by human vision systems. Models developed for images could also facilitate the study of self-organization principles underlying other complex sensory signals such as speech and video.
This research targets at a more fundamental understanding towards image modeling via nonlocal sparse representations (NSR). Unlike wavelet bases that are dilation and translation of a signal-independent wavelet function, the PI advocates the representation of a signal by ?basis functions? that are dilation and translation of the signal itself. Self-similarity based signal representation is closely related to the fractal theory and can be connected with sparse representations via regression shrinkage and selection. Such fruitful connection leads to a nonlocal regularization framework on graphical models and a class of novel deterministic annealing optimization techniques. This research has applications to a wide range of image processing systems from noise suppression in medical imaging to artifact removal in JPEG/JPEG2000 compression. The longer-term objective of the research is to demonstrate the intimate relationship between image processing and higher-level vision tasks such as segmentation and recognition.
