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，以从通过新兴的磁共振（MR）技术（称为部分并行成像（PPI））采集的数据生成图像。 已经开发了用于获得TV（全变差）正则化图像的几种快速算法，但是为了效率，要求底层矩阵满足特定性质，这不适用于PPI采集的数据。可应用于一般矩阵的算法对于真实的实际应用来说太慢。 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，一个是稀疏化问题，称为基追踪去噪问题，另一个是TV问题。 基追踪去噪问题的效率是使用有效集技术实现的，而TV问题的效率依赖于分裂，分裂将原始问题减少到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的研究还将为相关TV问题的解决提供算法的扩展，以获得更一般的图像类别。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，以非侵入性地可视化身体的内部结构和功能。与大多数其他模式相比，它在不同软组织之间提供了更好的对比度。 由于获取图像所需的时间，该技术的成本可能很高。此外，运动效应会导致图像退化。 PI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，这些算法有可能影响的应用程序，需要解决大型，病态，非光滑反演问题。