CIF:SMALL: Nonlocal Sparse Representations on Graphical Models: Theory, Algorithms and Applications

摘要图像处理是一个科学与工程交叉的跨学科领域。图像信号的数学建模不仅支持我们日常生活中的各种工程应用（例如，数码相机，高清电视，超声诊断等），而且还提供了一种计算方法来理解作为视觉皮层信息处理策略的感觉编码。提高对图像模型的理解可能会导致无伪影的信号处理系统，很好地匹配人类视觉系统的感知。为图像开发的模型也有助于研究其他复杂感官信号（如语音和视频）背后的自组织原理。本研究旨在通过非局部稀疏表示（NSR）对图像建模有更基本的理解。与小波基不同的是，小波基是一个与信号无关的小波函数的扩展和平移，PI主张用？基函数?那就是信号本身的膨胀和平移。基于自相似的信号表示与分形理论密切相关，可以通过回归收缩和选择与稀疏表示联系起来。这种卓有成效的联系导致了图形模型的非局部正则化框架和一类新的确定性退火优化技术。从医学成像中的噪声抑制到JPEG/JPEG2000压缩中的伪影去除，本研究广泛应用于图像处理系统。该研究的长期目标是证明图像处理与更高层次的视觉任务（如分割和识别）之间的密切关系。

AbstractImage 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.