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.

该项目的目的是开发方法，以比当前最新的方法相比，从测量范围少得多的测量结果和视频。 这种方法可用于大大降低对图像/视频进行测量非常昂贵的情况下的成像成本。 例如，在医学和神经科学研究中通常使用的磁共振成像（MRI）中就是这种情况。 这些方法还可以使从遥感，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，该项目将利用以前在压缩传感文献中证明棘手的信号结构的歧管模型。尽管歧管模型可以比通常的傅立叶/小波模型有效地表达许多信号的参数，从而可以完全重建这些信号，从较少的测量值中，歧管模型的复杂性已成为迄今为止的障碍。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，以允许将歧管模型用于压缩感测，而计算复杂性几乎没有提高。