PDE-based Image Restoration and Segmentation and Their Applications to Medical Imagery

研究者和他的同事们开发了新的扩散样pdemodel和计算方法，用于从超声、磁共振（MR）、计算机断层扫描（CT）、正电子发射断层扫描（PET）和单光子发射计算机断层扫描（SPECT）扫描仪获得的医学图像的图像恢复和分割。为了恢复，该项目研究了各种PDE模型和相关的数值程序，这些模型和程序可以有效地保存和恢复重要的图像特征，不仅是精细的结构，而且是缓慢的过渡，用于各种2D和3D医学图像。给定从变分方法衍生的基本模型，将开发非变分变量，通过集成噪声特性并结合适当的扩散调制器和动态约束项，以优化其在图像恢复中的性能。传统的Mumford-Shah函数分割的水平集公式对本质上的二值图像效果很好；然而，由于互补函数（分段卡通图像）计算的模糊性和检测平滑边界的能力，它们可能无法检测到一般图像所需的边缘。为了克服困难，该项目将开发各种数学和数值技术。创新的模型和计算算法将广泛影响其他各个领域，而增强的医学图像知识将推动医疗扫描仪设计的进步。该项目为平面和体积格式的医学图像开发了最先进的图像恢复和分割算法。尽管医学扫描仪的设计已经取得了显著的进步，但医学图像很容易包含某些噪声和各种伪影。为了进行准确的医学诊断，抑制这些伪影是极其重要的。另一方面，在各种现代医学诊断和手术中，计算机算法被用来自动检测和测量身体部位；然而，为了更准确地检测特征，这些算法还有待改进。研究者和他的同事研究了各种数学和计算算法，以提高图像质量和有效地分割重要的图像特征。此外，该计划将促进成像技术，以减少x射线计算机断层扫描（CT）对患者的辐射暴露。这里的目标是在达到所需的图像质量和医疗效益的同时，尽可能降低患者的CT辐射暴露。计划中的研究将对提高对当前数学图像处理技术的理解、推进医学图像知识和医学扫描仪设计的研究所进展产生重要影响。该研究项目将支持一名研究生，并加速密西西比州立大学一个名为“图像处理和计算技术”（IMPACT）的研究小组的活动，该小组由研究者组织。所有开发的软件都将与社区自由共享。

The investigator and his colleagues develop novel diffusion-like PDEmodels and computational methods for image restoration and segmentationof medical imagery acquired from ultrasound, magnetic resonance (MR),computed tomography (CT), positron emission tomography (PET), and singlephoton emission computed tomography (SPECT) scanners.For restoration, the project investigates various PDE models and relatednumerical procedures that can effectively preserve and restore importantimage features, not only fine structures but also slow transitions,for various medical images in 2D and 3D.Given basic models derived from variational approaches, non-variationalvariants will be developed in order to optimize their performancesin image restoration, by integrating noise characteristics and byincorporating appropriate diffusion modulators and dynamic constraintterms.Conventional level set formulations of the Mumford-Shah functional insegmentation work well for essentially binary images; however, they mayfail to detect desired edges for general images, due to ambiguity in thecomputation of the complementary function (the piecewise cartoon image)and the ability to detect smooth boundaries.In order to overcome the difficulty, the project will develop variousmathematical and numerical techniques.The innovative models and computational algorithms will broadly impactvarious other fields, while enhanced knowledge on medical images willinstitute advancements on medical scanner design.The project develops state-of-the-art algorithms in image restorationand segmentation for medical imagery in both planar and volumetric formats.Although there have been remarkable advancements in medical scanner design,medical images can easily incorporate certain noise and various artifacts.It is extremely important to suppress such artifacts for an accuratemedical diagnosis.On the other hand, in various modern medical diagnoses and operations,computer algorithms are being utilized to detect-and-measure body partsautomatically; however, these algorithms are yet to be improved for moreaccurate feature detection.The investigator and his colleagues study various mathematical andcomputational algorithms in order to enhance the image quality andsegment important image features effectively.Besides, the project will advance imaging techniques for the reductionof radiation exposure to the patient at X-ray computed tomography (CT).Here the goal is to keep patient radiation exposures from CT as low aspossible while achieving the required image quality and medical benefit.The planned research will have an important impact on improvedunderstanding of the current mathematical image processing techniques,advance knowledge on medical images, and institute advancements onmedical scanner design.The research project will support a graduate student and accelerateactivities in a research group at Mississippi State University, calledthe IMage Processing And Computational Techniques (IMPACT) which isorganized by the investigator.All developed software will be freely shared with the community.