论文标题
用于基于PDE的图像压缩的最佳插值数据
Optimal Interpolation Data for PDE-based Compression of Images with Noise
论文作者
论文摘要
我们介绍和讨论基于形状的模型，以在用噪声压缩图像中找到最佳的插值数据。目的是通过使用时间依赖的PDE介入来最大程度地减少图像及其重建对应物之间的$ l^2 $ norm中数据拟合项的丢失区域。我们从两种不同的角度分析了$γ$ - 联合的框架中提出的模型。首先，我们考虑通过关注离散时间依赖性PDE的第一次迭代而获得的连续固定PDE模型，并通过拓扑渐近方法获得有关每个像素的“相关性”的点信息。其次，我们基于“脂肪像素”（带正半径的球）引入了连续模型的有限维度设置，并通过$γ$ - 连续性研究半径消失时的渐近性。介绍了数值计算，以确认我们的理论发现对非平稳PDE基于基于PDE的图像压缩的有用性。
We introduce and discuss shape-based models for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of minimizing a data fitting term in the $L^2$-norm between the images and their reconstructed counterparts using time-dependent PDE inpainting. We analyze the proposed models in the framework of the $Γ$-convergence from two different points of view. First, we consider a continuous stationary PDE model, obtained by focusing on the first iteration of the discretized time-dependent PDE, and get pointwise information on the "relevance" of each pixel by a topological asymptotic method. Second, we introduce a finite dimensional setting of the continuous model based on "fat pixels" (balls with positive radius), and we study by $Γ$-convergence the asymptotics when the radius vanishes. Numerical computations are presented that confirm the usefulness of our theoretical findings for non-stationary PDE-based image compression.
