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.