We study the recovery of training data from overparameterized autoencoder
models. Given a degraded training sample, we define the recovery of the
original sample as an inverse problem and formulate it as an optimization task.
In our inverse problem, we use the trained autoencoder to implicitly define a
regularizer for the particular training dataset that we aim to retrieve from.
We develop the intricate optimization task into a practical method that
iteratively applies the trained autoencoder and relatively simple computations
that estimate and address the unknown degradation operator. We evaluate our
method for blind inpainting where the goal is to recover training images from
degradation of many missing pixels in an unknown pattern. We examine various
deep autoencoder architectures, such as fully connected and U-Net (with various
nonlinearities and at diverse train loss values), and show that our method
significantly outperforms previous methods for training data recovery from
autoencoders. Importantly, our method greatly improves the recovery performance
also in settings that were previously considered highly challenging, and even
impractical, for such retrieval.

我们研究了从超参数化自编码器模型中恢复训练数据的方法，通过将退化的训练样本定义为逆问题，并将其作为优化任务进行建模，我们使用训练好的自编码器隐式地定义特定训练数据集的正则化器，然后将复杂的优化任务转化为一个实用的方法，该方法迭代地应用训练好的自编码器和相对简单的计算来估计和处理未知的退化操作器，并在盲目修复中取得重要成果，显著超越以往的自编码器训练数据恢复方法，在先前被认为是高度挑战乃至不切实际的情景中也大大提高了恢复性能。

过参数化自编码器训练数据的恢复：逆问题视角

Recovery of Training Data from Overparameterized Autoencoders: An  Inverse Problem Perspective

Blind inpainting is a task to automatically complete visual contents without
specifying masks for missing areas in an image. Previous works assume missing
region patterns are known, limiting its application scope. In this paper, we
relax the assumption by defining a new blind inpainting setting, making
training a blind inpainting neural system robust against various unknown
missing region patterns. Specifically, we propose a two-stage visual
consistency network (VCN), meant to estimate where to fill (via masks) and
generate what to fill. In this procedure, the unavoidable potential mask
prediction errors lead to severe artifacts in the subsequent repairing. To
address it, our VCN predicts semantically inconsistent regions first, making
mask prediction more tractable. Then it repairs these estimated missing regions
using a new spatial normalization, enabling VCN to be robust to the mask
prediction errors. In this way, semantically convincing and visually compelling
content is thus generated. Extensive experiments are conducted, showing our
method is effective and robust in blind image inpainting. And our VCN allows
for a wide spectrum of applications.

本文提出了一种新的盲目修复网络，使训练过程在未知的缺失区域模式下更加鲁棒，并且通过语义不一致性的估计和新的空间归一化方法，使视觉修复更加精细，实验表明该方法在盲目图像修复方面相当有效。

VCNet: 盲目图像修复的强健方法

VCNet: A Robust Approach to Blind Image Inpainting

This article studies the problem of image restoration of observed images
corrupted by impulse noise and mixed Gaussian impulse noise. Since the pixels
damaged by impulse noise contain no information about the true image, how to
find this set correctly is a very important problem. We propose two methods
based on blind inpainting and $\ell_0$ minimization that can simultaneously
find the damaged pixels and restore the image. By iteratively restoring the
image and updating the set of damaged pixels, these methods have better
performance than other methods, as shown in the experiments. In addition, we
provide convergence analysis for these methods, these algorithms will converge
to coordinatewise minimum points. In addition, they will converge to local
minimum points (or with probability one) with some modifications in the
algorithms.

本文针对混合高斯脉冲噪声和脉冲噪声影响的图像修复问题，提出了基于盲填补和 $l_0$ 最小化的两种方法，可以同时找到受损像素并恢复图像。通过迭代恢复图像和更新受损像素集合，这些方法表现更优，实验结果和收敛分析均支持本文做法。