基于稀疏投影数据的模板图像重建
Template-Based Image Reconstruction from Sparse Tomographic Data
AI总结：
本文提出了一种变分正则化方法，用于从间接且噪声的测量数据中进行基于模板的图像重建，如在X射线计算机断层扫描中。通过变形给定的模板图像来重建图像，并将图像配准直接融入变分正则化方法中，以建模从模板到未知重建的质或强度保持传输。理论结果证明了在两种情况下最小化者的存在、数据稳定性以及噪声消失时的收敛性。数值上，通过扩展现有拉格朗日方法并提出多级方法来解决该问题，适用于当操作符和测量数据可以提供合适下采样过程时。最后，我们展示了在高度欠采样和噪声的Radon变换数据中基于模板的图像重建性能，并比较了质量保持和强度保持图像配准、各种正则化功能和不同距离函数的结果。我们的结果表明，当只有少量测量数据可用时可以得到非常合理的重建，并且当模板和未知图像之间的图像强度差异较大时，使用基于归一化互相关距离的方法具有优势。
摘要：
我们提出了一种变分正则化方法，用于从间接且噪声的测量数据中进行基于模板的图像重建，如在X射线计算机断层扫描中。通过变形给定的模板图像来重建图像，并将图像配准直接融入变分正则化方法中，以建模从模板到未知重建的质或强度保持传输。我们为这两种情况提供了变分正则化的理论结果。特别是，我们证明了在上述方程被施加且使用更一般距离函数时，最小化者的存在、数据稳定性以及噪声消失时的收敛性。数值上，我们通过扩展现有的拉格朗日方法来解决该问题，并提出了一种多级方法，适用于当操作符和测量数据可以提供合适下采样过程时。最后，我们展示了在高度欠采样和噪声的Radon变换数据中基于模板的图像重建性能。我们比较了质量保持和强度保持图像配准、各种正则化功能和不同距离函数的结果。我们的结果表明，当只有少量测量数据可用时可以得到非常合理的重建，并且当模板和未知图像之间的图像强度差异较大时，使用基于归一化互相关距离的方法具有优势。
英文摘要：
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
