Low-rank based models are proved outstanding for denoising on the data with strong repetitive or redundant property. However, for natural images with complex structures or rich details, the performance drops down because of the weak low-rankness of the data. A feasible solution is to transform the data into a suitable domain to further explore the underlying low-rank information. In this paper, we present a novel approach to create such a domain via a fully replicated linear autoencoder network. By applying various low-rank models to the feature maps generated by the encoder rather than the original data, and then performing inverse transformation by the decoder, their denoising performances all get enhanced. In addition, feature maps also show good sparsity, hence we introduce a new measure combining sparse and low-rank regularity, and further propose corresponding single image denoising model. Extensive experiments show the superiority of our work.

中文翻译：

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用于图像去噪的变换特征图域的低秩分解

事实证明，基于低秩的模型在对具有强重复或冗余属性的数据进行去噪方面表现出色。然而，对于结构复杂或细节丰富的自然图像，由于数据的低秩性较弱，性能下降。一个可行的解决方案是将数据转换为合适的域，以进一步探索底层的低秩信息。在本文中，我们提出了一种通过完全复制的线性自动编码器网络创建这样一个域的新方法。通过将各种低秩模型应用于编码器生成的特征图而不是原始数据，然后由解码器进行逆变换，它们的去噪性能都得到了增强。此外，特征图也表现出良好的稀疏性，因此我们引入了一种结合稀疏和低秩正则性的新度量，并进一步提出相应的单幅图像去噪模型。大量的实验显示了我们工作的优越性。