广义全变差的渐近性
Asymptotic behaviour of total generalised variation
摘要：
最近推出的二阶总广义变分泛函$\mathrm{TGV}_{β,α}^{2}$已成功的正则化图像处理的目的。其定义涉及两个正参数$α$和$β$，其值确定正则化的量和质量。在本文中，我们报告的行为$\mathrm{TGV}_{β,α}^{2}$的情况下，参数$α, β$以及它们的比率$β/α$变得非常大或非常小。其中，我们证明了充分对称的二维数据和大比例$β/α$，$\mathrm{TGV}_{β,α}^{2}$正则化符合全变差（$\mathrm{TV}$）正则化。
英文摘要：
The recently introduced second order total generalised variation functional $\mathrm{TGV}_{β,α}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $α$ and $β$ whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of $\mathrm{TGV}_{β,α}^{2}$ in the cases where the parameters $α, β$ as well as their ratio $β/α$ becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio $β/α$, $\mathrm{TGV}_{β,α}^{2}$ regularisation coincides with total variation ($\mathrm{TV}$) regularisation.
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