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

最后修改日期：05/19/08最后修改人：Sheila M.史密斯 摘要摘要许多成像任务涉及不适定问题，这需要现实的先验知识。标准的凸优化技术使用偏好全局平滑图像的先验，因此倾向于给出差的结果。图切割方法，允许边缘保持先验的一类有限的不适定问题，已被证明是相当成功的，在过去的十年。这个研究项目将解决一类重要但具有挑战性的不适定问题，即秩亏线性逆系统所产生的问题。这样的欠约束问题出现在医学成像任务中，例如MRI CT图像重建和fMRI去失真，以及在传统的视觉问题中，例如超分辨率。目前，这些应用程序依赖于凸优化方法，不支持现实的图像先验。然而，现有的图切割方法不能应用由于一些困难的理论问题。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。我们将开发新的图形结构来解决线性逆系统，大量借鉴布尔优化的最先进技术。为了简化我们的任务，我们将利用感兴趣的应用中出现的秩亏线性逆系统的特定属性。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，包含了驱动我们工作的所有应用程序。虽然我们提出的工作强调算法开发，但我们也将对一系列应用程序上的新算法进行重要的实验评估，以评估其性能并确定有前途的新途径。该项目汇集了计算机视觉，医学成像和图形算法的专家，以新颖的方式解决广泛关注的问题。我们所关注的线性逆系统出现在广泛的医疗应用以及其他领域，但当前的技术存在显着缺陷。我们的方法在很大程度上借鉴了研究人员在过去十年中开发的方法，这些方法在相关问题上已经证明是非常成功的。此外，该项目将加强计算机视觉和算法研究人员之间的联系，这对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