论文标题
非本地边界变化与应用
Nonlocal Bounded Variations with Applications
论文作者
论文摘要
本文研究了跨维度子集越过较低的子集和尖锐的过渡的问题，本文研究了分数有限变化（$ bv $） - 类型空间的特性。 考虑了经典$ bv $的两个不同的天然分数类似物：$ bv^α$，这是Comi-Stefani最近研究的Riesz-Fractional梯度引起的空间；和$ bv^α$，是由Gagliardo-type的分数梯度通常用于迪里奇特形式和perideNangics的 - 这与Caffarelli-Roquejoffre-savin分数周长自然相关。我们的主要理论结果是后者$ bv^α$实际上对应于gagliardo-slobodeckij space $ w^{α，1} $。作为一种应用，使用这些空间的属性，引入了新型的图像denoising模型，并得出了它们相应的Fenchel预双重配方。后者需要具有紧凑的支撑的光滑功能密度。我们为凸形域建立了此密度属性。
Motivated by problems where jumps across lower dimensional subsets and sharp transitions across interfaces are of interest, this paper studies the properties of fractional bounded variation ($BV$)-type spaces. Two different natural fractional analogs of classical $BV$ are considered: $BV^α$, a space induced from the Riesz-fractional gradient that has been recently studied by Comi-Stefani; and $bv^α$, induced by the Gagliardo-type fractional gradient often used in Dirichlet forms and Peridynamics - this one is naturally related to the Caffarelli-Roquejoffre-Savin fractional perimeter. Our main theoretical result is that the latter $bv^α$ actually corresponds to the Gagliardo-Slobodeckij space $W^{α,1}$. As an application, using the properties of these spaces, novel image denoising models are introduced and their corresponding Fenchel pre-dual formulations are derived. The latter requires density of smooth functions with compact support. We establish this density property for convex domains.
