CIF: Small: Kernel Trick Compressive Sensing

该项目的目标是开发一种方法，通过比目前最先进的技术更少的测量来获取真实世界的图像和视频。在目前测量图像/视频非常昂贵的情况下，这些方法可用于大大降低成像成本。例如，通常用于医学和神经科学研究的磁共振成像（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，该项目将利用以前在压缩感知文献中被证明难以处理的信号结构的多种模型。虽然流形模型可以比通常的傅立叶/小波模型用更少的参数有效地表达许多信号，允许从更少的测量中完全重建这些信号，但流形模型的复杂性迄今为止一直是其在有效数据采集中使用的障碍。该项目将采用一个优雅的框架，基于机器学习中核方法中常用的核技巧，允许使用流形模型进行压缩感知，而计算复杂性几乎没有增加。

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.