Iterative Methods in Image Reconstruction

研究者开发了高效可靠的迭代方法，用于从记录的嘈杂数据中重建图像。为了获得更好的分辨率图像，他开发了能够有效处理复杂算子（例如，空间变核）的方法和强制非负性约束的方法。越来越复杂的成像设备的出现产生了新一代非常困难的计算问题，其中从记录数据重建图像。例如，在乳腺癌检测中，需要在获得高分辨率图像和限制对患者的辐射剂量之间进行权衡，就会出现这样的问题。最近还提出了用于三维成像的新设备，其中高维数和分辨率要求导致非琐碎的计算复杂性。另一个例子是使用自适应光学技术的新型地基望远镜。为了提取详细信息并利用新成像设备可以获得的分辨率的增加，重要的是要开发考虑成像机制中属性的空间变化的方法，这是不适合基于标准快速傅里叶变换的方法的。新的全三维医学成像设备需要新一代的计算方法来有效地从记录数据中重建图像，为了使这些新的计算方法找到临床使用的方式，重要的是提供易于实施和实验的软件包。开发了在计算解中强制非负性的方法，并且可以有效地处理空间变化的核。在这个项目中开发的许多计算工具应该适用于广泛的迭代图像重建方法，包括线性，非线性和基于统计的方法。

The investigator develops efficient and reliable iterativemethods for reconstructing an image from recorded, noisy data.To obtain better resolved images, he develops methods that caneffectively handle complicated operators (e.g., spatially variantkernels) and methods that enforce a nonnegativity constraint. The emergence of increasingly sophisticated imaging deviceshas produced a new generation of very difficult computationalproblems in which an image is to be reconstructed from recordeddata. Such problems arise, for example, in breast cancerdetection, where there is a tradeoff between the needs to obtainhigh resolution images and to limit the radiation dose to thepatient. New devices have also been recently proposed for3-dimensional imaging, where high dimensionality and resolutionrequirements result in nontrivial computational complexity. Yetanother example occurs in new ground-based telescopes, which useadaptive optics techniques. To extract detailed information andtake advantage of the increase in resolution that can be obtainedfrom new imaging devices, it is important to develop methods thattake into account spatial changes of properties in the imagingmechanisms, which are not amenable to standard fast Fouriertransform based methods. New fully 3-dimensional medical imagingdevices require a new generation of computational methods toefficiently reconstruct images from recorded data, and in orderfor these new computational methods to find their way to clinicaluse, it is important to provide software packages that allow foreasy implementation and experimentation. Methods that enforcenonnegativity in the computed solution, and that can efficientlyhandle spatially variant kernels, are developed. Many of thecomputational tools developed in this project should beapplicable to a wide class of iterative image reconstructionmethods, including linear, nonlinear and statistical basedmethods.