The explicit low-rank regularization, e.g., nuclear norm regularization, has
been widely used in imaging sciences. However, it has been found that implicit
regularization outperforms explicit ones in various image processing tasks.
Another issue is that the fixed explicit regularization limits the
applicability to broad images since different images favor different features
captured by different explicit regularizations. As such, this paper proposes a
new adaptive and implicit low-rank regularization that captures the low-rank
prior dynamically from the training data. The core of our new adaptive and
implicit low-rank regularization is parameterizing the Laplacian matrix in the
Dirichlet energy-based regularization, which we call the regularization AIR.
Theoretically, we show that the adaptive regularization of \ReTwo{AIR} enhances
the implicit regularization and vanishes at the end of training. We validate
AIR's effectiveness on various benchmark tasks, indicating that the AIR is
particularly favorable for the scenarios when the missing entries are
non-uniform. The code can be found at this https URL.

本文提出了一种自适应的隐式低秩正则化方法，通过从训练数据中动态捕捉低秩先验来解决固定正则化的局限性，并通过实验验证表明其在各个数据集上都有优秀的表现。

矩阵完成的自适应和隐式正则化

Adaptive and Implicit Regularization for Matrix Completion

Face completion is a challenging generation task because it requires
generating visually pleasing new pixels that are semantically consistent with
the unmasked face region. This paper proposes a geometry-aware Face Completion
and Editing NETwork (FCENet) by systematically studying facial geometry from
the unmasked region. Firstly, a facial geometry estimator is learned to
estimate facial landmark heatmaps and parsing maps from the unmasked face
image. Then, an encoder-decoder structure generator serves to complete a face
image and disentangle its mask areas conditioned on both the masked face image
and the estimated facial geometry images. Besides, since low-rank property
exists in manually labeled masks, a low-rank regularization term is imposed on
the disentangled masks, enforcing our completion network to manage occlusion
area with various shape and size. Furthermore, our network can generate diverse
results from the same masked input by modifying estimated facial geometry,
which provides a flexible mean to edit the completed face appearance. Extensive
experimental results qualitatively and quantitatively demonstrate that our
network is able to generate visually pleasing face completion results and edit
face attributes as well.

本文提出了一种基于面部几何特征的面部完成和编辑网络（FCENet），通过从未误差处理的人脸区域分析面部几何结构，采用编码器 - 解码器结构和低秩正则化项进行脸部图像的自动修复和编辑。