CIF: Small: Kernel Trick Compressive Sensing

CIF：小：内核技巧压缩感知

• 批准号: 1117775
• 负责人: Shannon Hughes
• 金额: $ 42.58万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117775&HistoricalAwards=false
• 关键词: CIF; Small; Kernel; Trick; Compressive

The goal of this project is to develop methods to acquire real-world images and video from far fewer measurements than is possible in the current state-of-the-art. Such methods could be used to greatly reduce the cost of imaging in situations where taking measurements of an image/video is currently very expensive. This is the case, for example, in magnetic resonance imaging (MRI), commonly used in both medicine and neuroscientific research. These methods could also make possible the acquisition of much more detailed information from the same imaging resources in areas such as remote sensing, geoscience, or astronomy. To achieve this goal, the project will exploit manifold models for signal structure that have previously proved intractable in the compressive sensing literature. While manifold models can efficiently express many signals in terms of dramatically fewer parameters than the usual Fourier/wavelet models, allowing for complete reconstruction of these signals from dramatically fewer measurements, the complexity of manifold models has to date stood as an obstacle to their use in efficient data acquisition. This project will employ an elegant framework, based on the kernel trick commonly used in kernel methods in machine learning, to permit the use of manifold models for compressive sensing with little to no increase in computational complexity.

该项目的目标是开发方法，以获取现实世界的图像和视频从远少于测量是可能的，在目前的最先进的。这种方法可以用来大大降低成像的情况下，采取测量的图像/视频的成本目前非常昂贵。 例如，在医学和神经科学研究中常用的磁共振成像（MRI）就是这种情况。 这些方法还可以从遥感、地球科学或天文学等领域的相同成像资源中获取更详细的信息。 为了实现这一目标，该项目将利用多种信号结构模型，这些模型以前在压缩感知文献中被证明是难以解决的。虽然流形模型可以有效地表达许多信号的参数显着减少比通常的傅立叶/小波模型，允许这些信号的完全重建从显着减少测量，流形模型的复杂性，迄今为止，他们的使用在有效的数据采集的障碍。该项目将采用一个优雅的框架，基于机器学习中内核方法中常用的内核技巧，允许使用流形模型进行压缩感知，而计算复杂度几乎没有增加。