Learning of translation-invariant image model with subspace sparsity and its applications to image processing

在这项研究中，提出了基于子空间稀疏的图像模型。针对图像恢复问题，提出了综合图像模型和分析图像模型。对于图像合成模型，图像被近似为平移生成原子的线性组合，这些原子代表图像的微观结构。为了学习局部结构，同时对平移原子的数目和生成原子所跨越的子空间施加稀疏性。将所学习的生成原子成功地应用于单图像超分辨率问题。在图像分析模型中，引入非线性滤波器来定义图像的子空间。通过最小化定义在图像的子空间和退化图像之间的范数来实现图像恢复问题。将所提出的非线性分析模型应用于去噪问题。与线性分析模型相比，该模型获得了上级的结果。

In this study, image models based on subspace sparsity is proposed. Both the synthesis and analysis image model are proposed for image recovery problem. For image synthesis model, an image is approximated as a linear combination of translated generating atoms, which represent micro structures of the image. In order to learn the local structures, the sparsity is imposed on the numbers of the translated atoms and the subspaces that are spanned by the generating atoms simultaneously. The learnt generating atoms are successfully applied to single-image super resolution problem. For image analysis model, nonlinear filters are introduced to definition of the subspace of images. The image recovery problem is achieved by minimizing the norm that is defined between the subspace of the image and the degraded image. The proposed nonlinear analysis model is applied to denoisng problem. The proposed model obtains superior results comparing with the linear analysis model.