In many imaging applications where segmented features (e.g. blood vessels)
are further used for other numerical simulations (e.g. finite element
analysis), the obtained surfaces do not have fine resolutions suitable for the
task. Increasing the resolution of such surfaces becomes crucial. This paper
proposes a new variational model for solving this problem, based on an
Euler-Elastica-based regulariser. Further, we propose and implement two
numerical algorithms for solving the model, a projected gradient descent method
and the alternating direction method of multipliers. Numerical experiments
using real-life examples (including two from outputs of another variational
model) have been illustrated for effectiveness. The advantages of the new model
are shown through quantitative comparisons by the standard deviation of
Gaussian curvatures and mean curvatures from the viewpoint of discrete
geometry.

在多种成像应用中，对于进一步用于其他数值模拟的分割特征（例如血管），所获得的曲面分辨率不足以满足任务要求。本文提出了一种基于 Euler-Elastica 的正则化方法的新变分模型来解决这个问题，并提出和实施了两种求解模型的数值算法，即投影梯度下降法和交替方向乘子法。通过实际例子的数值实验（其中包括另一个变分模型的输出），证明了该模型的有效性。从离散几何的角度，通过高斯曲率和平均曲率的标准差进行了定量比较，展示了新模型的优势。

通过少数低分辨率切片实现超分辨率表面重建

Super-Resolution Surface Reconstruction from Few Low-Resolution Slices

Learned data models based on sparsity are widely used in signal processing
and imaging applications. A variety of methods for learning synthesis
dictionaries, sparsifying transforms, etc., have been proposed in recent years,
often imposing useful structures or properties on the models. In this work, we
focus on sparsifying transform learning, which enjoys a number of advantages.
We consider multi-layer or nested extensions of the transform model, and
propose efficient learning algorithms. Numerical experiments with image data
illustrate the behavior of the multi-layer transform learning algorithm and its
usefulness for image denoising. Multi-layer models provide better denoising
quality than single layer schemes.

本论文研究了基于稀疏性的数据模型在信号处理和成像应用中的应用。特别关注了稀疏变换学习，提出了基于多层分层扩展的学习算法，并在图像去噪的数值实验中证明了其有效性。多层模型比单层方案具有更好的去噪质量。