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.

稀疏信号测序研究的递归重建研究重点是递归算法，用于在因果重建（大约）（大约）稀疏信号的时间序列（少量````''''不一致的线性投影中的稀疏信号。算法将在Intervention-MRI（MRI）中使用算法在Intervention-Mixriigation-trime time Dyname consrigiatientiation-trimientiation-trimiention-trimientiation-trimientiation-trimientiation-trimientiation-MRI中或在Intervention-ivection-Myliology中使用。由于其“相对较慢的图像获取”，MRI目前不可用（大型数据获取时间和/或缓慢的图像重建算法）。 CS一个GO共同重建整个时间顺序。替代方案 - 每次CS（Simpleecs） - 需要更多的测量。这项研究是第一个开发和分析信号序列重建的递归算法的研究，这些算法与简单CS具有相同的复杂性，但是（a）使用与简单CS所需的无噪声测量更少的无噪声测量来实现精确的重建； （b）在使用嘈杂的测量值时，实现比简单CS的重建误差要小，尤其是当测量数量较小时； （c）随着时间的推移证明是稳定的（重建误差保持界限）。更少的测量意味着减少MRI的扫描时间，而递归重建意味着实时成像是可能的。通过利用稀疏性模式随着时间的流逝而缓慢变化的事实，该问题被提出为具有部分已知支持的压缩感之一。CS和顺序CS被纳入研究生/本科课程中，并在适当的水平上纳入高级设计。