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

CIF:SMALL：图形模型的非局部稀疏表示：理论、算法和应用

• 批准号: 0914353
• 负责人: Xin Li
• 金额: $ 17.25万
• 依托单位: West Virginia University Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-15 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0914353&HistoricalAwards=false
• 关键词: CIF; SMALL; Nonlocal; Sparse; Representations

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.

图像处理是一个科学与工程交叉的交叉学科。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、高清晰度电视、超声波诊断等），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。对图像模型的更好理解可能会导致无伪影的信号处理系统，其很好地匹配人类视觉系统的感知。为图像开发的模型还可以促进对语音和视频等其他复杂感官信号的自组织原理的研究。这项研究的目标是通过非局部稀疏表示（NSR）对图像建模进行更基本的理解。不像小波基的膨胀和平移的信号无关的小波函数，PI主张表示的信号？基函数？就是信号本身的膨胀和平移基于自相似性的信号表示与分形理论密切相关，并且可以通过回归收缩和选择与稀疏表示联系起来。这种富有成效的连接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。这项研究具有广泛的应用范围，从医学成像中的噪声抑制到JPEG/JPEG 2000压缩中的伪影去除的图像处理系统。这项研究的长期目标是证明图像处理和更高层次的视觉任务（如分割和识别）之间的密切关系。