CCF (CIF): Small: Recursive Reconstruction of Sparse Signal Sequences

CCF (CIF)：小：稀疏信号序列的递归重建

• 批准号: 0917015
• 负责人: Namrata Vaswani
• 金额: $ 27.93万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0917015&HistoricalAwards=false
• 关键词: CCF; CIF; Small; Recursive; Reconstruction

Recursive Reconstruction of Sparse Signal SequencesThis research focuses on recursive algorithms for causally reconstructing a time sequence of (approximately) sparse signals from a small number of ``incoherent" linear projections. The algorithms will be useful for real-time dynamic magnetic resonance imaging (MRI) in interventional radiology applications such as image-guided surgery or in functional-MRI. MRI is currently not usable for such real-time applications due to its "relatively slow image acquisition" (large data acquisition times and/or slow image reconstruction algorithms). Other potential applications include dynamic tomography for solar imaging or real-time single-pixel video imaging.Since the recent introduction of compressive sensing (CS), the static version of the above problem has been thoroughly studied. But most existing algorithms for the dynamic problem just use CS to jointly reconstruct the entire time sequence in one go. This is a batch solution and has very high complexity. The alternative - CS at each time (simpleCS) - requires many more measurements. This research is the first to develop and analyze recursive algorithms for signal sequence reconstruction, which have the same complexity as simple CS, but which (a) achieve exact reconstruction using much fewer noise-free measurements than those needed by simple CS; (b) achieve provably smaller reconstruction error than simple CS, when using noisy measurements, especially when the number of measurements is small; and (c) are provably stable over time (reconstruction error remains bounded). Fewer measurements means reduced scan times for MRI, while recursive reconstruction means real-time imaging is possible. By exploiting the fact that sparsity patterns change slowly over time, the problem is formulated as one of compressive sensing with partially known support.CS and sequential CS are incorporated into the graduate/undergraduate curriculum and into senior-design at appropriate levels.

稀疏信号序列的递归重建这项研究重点是递归算法，用于从少量“不相干”线性投影中因果地重建（近似）稀疏信号的时间序列。该算法将可用于实时动态磁共振成像（MRI） ）在图像引导手术或功能性 MRI 等介入放射学应用中，由于其“相对较慢”，目前无法用于此类实时应用。图像采集”（大数据采集时间和/或缓慢的图像重建算法）。其他潜在应用包括用于太阳成像或实时单像素视频成像的动态层析成像。自从最近引入压缩传感（CS）以来，静态版本上述问题的研究已经很深入，但是现有的动态问题算法大多只是使用CS一次性联合重建整个时间序列，这是一种批量解决方案，具有非常高的复杂度。另一种选择 - 每次 CS (simpleCS) - 需要更多的测量。这项研究首次开发和分析了信号序列重建的递归算法，该算法具有与简单 CS 相同的复杂性，但 (a) 使用比简单 CS 所需的少得多的无噪声测量来实现精确重建； (b) 当使用噪声测量时，特别是当测量数量较少时，可实现比简单 CS 更小的重建误差； （c）随着时间的推移可证明是稳定的（重建误差仍然有限）。更少的测量意味着减少 MRI 扫描时间，而递归重建意味着可以实现实时成像。通过利用稀疏模式随时间缓慢变化的事实，该问题被表述为具有部分已知支持的压缩感知问题。CS 和顺序 CS 被纳入研究生/本科生课程以及适当级别的高级设计中。