论文标题
在具有噪音的图像中选择最佳的插值数据
Choosing The Best Interpolation Data in 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，以在压缩具有噪声的图像时找到最佳的插值数据。目的是通过将图像及其重建的对应物之间的$ l^2 $ norm中的数据拟合项最小化来重建丢失区域。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，我们考虑一个连续的固定PDE模型，并通过拓扑渐近方法获取有关每个像素的“相关性”的指定信息。其次，我们将有限的维度设置在基于脂肪像素的连续模型中（带正半径为正的球）中，然后通过$γ$ - 连续性研究半径消失时的渐近性。我们将方法扩展到了基于时间依赖的重建，并讨论了选择掩模内插值数据的几种策略，这些数据可能会改进迭代。介绍了数值计算，以确认我们的理论发现对基于固定和非平稳PDE的图像压缩的有用性。
We introduce and discuss shape based models for finding the best interpolation data in compression of images with noise. The aim is to reconstruct missing regions by means of minimizing data fitting term in the $L^2$-norm between the images and their reconstructed counterparts. We analyse the proposed models in the framework of the $Γ$-convergence from two different points of view. First, we consider a continuous stationary PDE model and get pointwise information on the "relevance" of each pixel by a topological asymptotic method. Second, we introduce a finite dimensional setting into the continuous model based on fat pixels (balls with positive radius), and we study by $Γ$-convergence the asymptotics when the radius vanishes. We extend the method to time-dependent based reconstruction and discuss several strategies for choosing the interpolation data within masks that might be improved over the iterations. Numerical computations are presented that confirm the usefulness of our theoretical findings for stationary and non-stationary PDE-based image compression.
