RI-Medium: Collaborative Research: Graph Cut Algorithms for Linear Inverse Systems

最后修改日期：5/19/08最后修改人：Sheila M.Smith摘要许多成像任务涉及病态问题，这需要现实的先验。标准的凸优化技术使用优先于全局平滑图像的先验，因此往往给出较差的结果。图割方法允许对一类有限的不适定问题保持先验边，在过去的十年中被证明是相当成功的。这项研究项目将解决一类重要但具有挑战性的不适定问题，即由秩亏缺线性逆系统产生的问题。这种欠约束问题出现在医学成像任务中，如MRI和CT图像重建和fMRI不失真，以及传统的视觉问题，如超分辨率。目前，这些应用依赖于凸优化方法，而凸优化方法不支持真实图像先验。然而，现有的图割方法由于一些理论上的困难而无法应用。为了克服这些挑战，我们提出了计算机视觉研究人员和图形算法专家之间的合作。我们将开发新的图结构来解决线性逆系统，大量借鉴布尔优化的最新技术。为了简化我们的任务，我们将利用在感兴趣的应用中出现的秩亏差线性逆系统的特定性质。我们将主要关注稀疏结构线性逆系统，这是一个重要的子类，包含了推动我们工作的所有应用程序。虽然我们拟议的工作强调算法开发，但我们也将在一系列应用程序上对新算法进行重要的实验评估，以评估其性能并找到有前途的新途径。这个项目汇集了计算机视觉、医学成像和图形算法方面的专家，以一种新颖的方式解决人们广泛感兴趣的问题。我们所关心的线性逆系统出现在广泛的医学应用中，以及在其他领域，然而目前的技术有显著的缺点。我们的方法在很大程度上借鉴了调查人员在过去十年中开发的方法，事实证明，这些方法在相关问题上相当成功。此外，这个项目将加强计算机视觉和算法研究人员之间的联系，事实证明，这两个领域都非常有益。该项目产生的出版物和其他材料将在http://www.cs.cornell.edu/~rdz/graphcuts.html上提供

Last Modified Date: 05/19/08 Last Modified By: Sheila M. Smith Abstract Abstract Many imaging tasks involve ill-posed problems, which require realistic priors. Standard convex optimization techniques use priors that prefer globally smooth images, and thus tend to give poor results. Graph cut methods, which permit edge-preserving priors for a restricted class of ill-posed problems, have proven quite successful over the last decade. This research project will address an important but challenging class of ill-posed problems, namely those arising from rank-deficient linear inverse systems. Such underconstrained problems occur in medical imaging tasks such as MRI&CT image reconstruction and fMRI undistortion, as well as in traditional vision problems such as super- resolution. Currently these applications rely on convex optimization methods, which do not support realistic image priors. Yet existing graph cut methods cannot be applied due to some difficult theoretical issues. To overcome these challenges we propose a collaboration between computer vision researchers and experts in graph algorithms. We will develop new graph constructions to address linear inverse systems, drawing heavily on state-of-the-art techniques from boolean optimization. To simplify our task we will exploit specific properties of the rank-deficient linear inverse systems that arise in the applications of interest. We will focus primarily on sparse structured linear inverse systems, an important subclass which contains all of the applications that drive our work. While our proposed work stresses algorithm development, we will also do a significant experimental evaluation of new algorithms on a range of applications, both to assess their performance and to identify promising new avenues. This project brings together experts in computer vision, medical imaging and graph algorithms to address a problem of broad interest in a novel manner. The linear inverse systems that we are concerned with arise in a wide range of medical applications, as well as in other areas, yet current techniques have significant shortcomings. Our approach draws heavily on methods developed by the investigators over the last decade, which have proven quite successful for related problems. In addition, this project will strengthen the ties between researchers in computer vision and algorithms, which have proven to be quite beneficial to both areas. Publications and additional material resulting from this project will be made available at http://www.cs.cornell.edu/~rdz/graphcuts.html