Fast TV-Regularized Large-Scale and Ill-Conditioned Linear Inversion with Application to PPI

快速电视正则化大规模病态线性反演及其在 PPI 中的应用

• 批准号: 1115568
• 负责人: William Hager
• 金额: $ 24.16万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115568&HistoricalAwards=false
• 关键词: Fast; TV; Regularized; Large; Scale

The research of the PIs is focused on the development of new algorithms to generate images from data acquired through the emerging Magnetic Resonance (MR) technology known as Partially Parallel Imaging (PPI). Several fast algorithms for obtaining TV (total variation) regularized images have already been developed, but for efficiency require that the underlying matrices satisfy specific properties, that do not hold for PPI acquired data. Algorithms which can be applied for a general matrix are too slow for real time practical application. The goals of the PIs' research are to both study and compare recently developed fast methods, as well as to develop novel, fast and accurate algorithms suitable for general large-scale ill-conditioned inversion problems. Image reconstruction requires the fast solution of two problems, a sparsification problem known as the basis pursuit denoising problem, and a TV problem. Efficiency for the basis pursuit denoising problem is achieved using active set techniques, while efficiency for the TV problem relies on splittings which reduce the original problem into subproblems that can be solved quickly. Convergence and statistical reliability of the algorithms will be established. The PIs' research will also provide extensions of the algorithms for the solution of related TV-based problems for obtaining more general classes of images.This research has broad impact on Partially Parallel Magnetic Resonance imaging technology. Magnetic resonance imaging is commonly used in radiology to non-invasively visualize the internal structure and function of the body. It provides better contrast between the different soft tissues than most other modalities. Due to the time needed to acquire an image, the cost of this technology can be high. Also motion effects can lead to image degradation. The algorithms to be developed by the PIs will reduce scan time, while improving the accuracy of the reconstructed images. More generally, these algorithms have the potential for impact on applications which require the solution of large, ill conditioned, nonsmooth inversion problems.

PI 的研究重点是开发新算法，从通过新兴的磁共振 (MR) 技术（称为部分并行成像 (PPI)）获取的数据生成图像。 已经开发了几种用于获取 TV（全变分）正则化图像的快速算法，但为了提高效率，要求底层矩阵满足特定属性，而这不适用于 PPI 采集的数据。可应用于一般矩阵的算法对于实时实际应用来说太慢。 PI 研究的目标是研究和比较最近开发的快速方法，以及开发适用于一般大规模病态反演问题的新颖、快速和准确的算法。图像重建需要快速解决两个问题，一个是称为基追踪去噪问题的稀疏化问题，另一个是电视问题。 基追求去噪问题的效率是使用主动集技术实现的，而电视问题的效率则依赖于分裂，将原始问题减少为可以快速解决的子问题。将建立算法的收敛性和统计可靠性。 PI 的研究还将提供算法的扩展，用于解决相关的基于电视的问题，以获得更通用的图像类别。这项研究对部分并行磁共振成像技术具有广泛的影响。 磁共振成像通常用于放射学，以非侵入性方式显示身体的内部结构和功能。与大多数其他方式相比，它可以在不同软组织之间提供更好的对比度。 由于获取图像需要时间，因此该技术的成本可能很高。运动效果也会导致图像质量下降。 PI 将开发的算法将减少扫描时间，同时提高重建图像的准确性。 更一般地说，这些算法可能会对需要解决大型病态非平滑反演问题的应用产生影响。