论文标题
二阶总广义变化约束的反问题
Inverse problems with second-order Total Generalized Variation constraints
论文作者
论文摘要
最近，已将总体广义变异（TGV）作为惩罚功能引入，用于建模具有边缘和平滑变化的图像。可以将其解释为从第一个到$ k $ th的分销衍生品的最佳平衡的“稀疏”惩罚，并在应用于图像denoising时会带来理想的结果，即带有tgv罚款的$ l^2 $。目前的论文研究了二阶的TGV在解决不适合线性反问题的背景下。显示了关于数据的Tikhonov功能最小化解决方案的存在和稳定性，并将其应用于从模糊和嘈杂数据中恢复图像的问题。
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to the $k$-th distributional derivative and leads to desirable results when applied to image denoising, i.e., $L^2$-fitting with TGV penalty. The present paper studies TGV of second order in the context of solving ill-posed linear inverse problems. Existence and stability for solutions of Tikhonov-functional minimization with respect to the data is shown and applied to the problem of recovering an image from blurred and noisy data.
