论文标题
非本地$ bv $函数和具有$ l^1 $ fidelity的脱泽模型
Non-local $BV$ functions and a denoising model with $L^1$ fidelity
论文作者
论文摘要
我们研究了具有加权$ l^1 $ fidelity的一般总变化模型，其中正规术语是由合适的（不可汇总）内核$ k $引起的非本地变化，近似项给出了$ l^1 $规范，相对于非阳性级别的$ l^bounted $ l^$ l^$ l^f^uffty $ l^\ filtty $ l^\ infty $ denter。我们对具有有限的总$ k $变化的非本地$ bv $函数的空间进行了详细分析，并特别强调了紧凑，卢辛型型估计值，sobolev嵌入式以及$ k $ variation and Isoperimetietric and Monotonicity属性。最后，我们在这种非本地环境中处理了Cheeger集合的理论，并将其应用于模型中的忠诚度。
We study a general total variation denoising model with weighted $L^1$ fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel $K$, and the approximation term is given by the $L^1$ norm with respect to a non-singular measure with positively lower-bounded $L^\infty$ density. We provide a detailed analysis of the space of non-local $BV$ functions with finite total $K$-variation, with special emphasis on compactness, Lusin-type estimates, Sobolev embeddings and isoperimetric and monotonicity properties of the $K$-variation and the associated $K$-perimeter. Finally, we deal with the theory of Cheeger sets in this non-local setting and we apply it to the study of the fidelity in our model.
