Extensions to compressed sensing theory with application to dynamic MRI

数据采集或采样问题是数字信号处理的核心。长期以来，人们一直认为应该获得足够数量的样本来满足所谓的奈奎斯特标准。然后离散采样信号是原始模拟信号的等效表示。然而，最近，压缩感知的范式挑战了这一想法。如果已知信号具有结构，并且几乎所有信号都具有结构，则可以使用此方法减少定义信号所需的样本数量；压缩感知提倡以信息速率采样，而不是奈奎斯特速率。该项目旨在扩展现有的压缩感知理论，以包括更一般的先进信号模型，特别是多分辨率图像模型。这些想法应该对采样数据困难的问题产生重大影响，因为采样数据耗时、昂贵或存在相关的安全问题（例如患者暴露于电磁辐射）。该项目将进一步探索压缩传感作为一种可能用于分布式或遥感应用的新型压缩策略的潜力。该项目将利用这些想法开发新的快速磁共振成像（MRI）采集系统。加速扫描时间的优点是多方面的。它使临床医生能够进行更高分辨率的扫描，并获得更详细的动态图像序列（例如用于心脏诊断）。此外，随着高场扫描仪使用的增加，减少给定图像采集的样品具有降低患者遭受的射频暴露的额外好处。

The problem of data acquisition or sampling lies at the heart of digital signal processing. It has been a long held belief that one should acquire a sufficient number of samples to satisfy the so-called Nyquist criterion. Then the discretely sampled signal is an equivalent representation of the original analogue one. However, recently, the paradigm of compressed sensing has challenged this idea. If a signal is known to have structure, and almost all signals do, then this can be used to reduce the number of samples required to define the signal; compressed sensing advocates sampling at the information rate not the Nyquist rate . This project aims to extend the existing theory of compressed sensing to include more general advanced signal models and, in particular, multi-resolution image models. These ideas should have a big impact on problems where sampling data is difficult either because it is time consuming, expensive or has associated safety issues (e.g. patient exposure to electromagnetic radiation). The project will further explore the potential of compressed sensing as a novel compression strategy for possible use in distributed or remote sensing applications. The project will use these ideas to develop new rapid Magnetic Resonance Imaging (MRI) acquisition systems. The advantages of accelerated scan times are manifold. It enables clinicians to take higher resolution scans and to acquire more detailed dynamic image sequences (e.g. for cardiac diagnosis). Furthermore, with the trend to the increased use of high field scanners reducing the samples for a given image acquisition has the additional benefit of lowering the RF exposure that the patient is subjected to.