IEEE Trans Pattern Anal Mach Intell. 2012 Jan;34(1):19-32. doi: 10.1109/TPAMI.2011.87. Epub 2011 May 12.
We address the problem of blind separation of multiple source layers from their linear mixtures with unknown mixing coefficients and unknown layer motions. Such mixtures can occur when one takes photos through a transparent medium, like a window glass, and the camera or the medium moves between snapshots. To understand how to achieve correct separation, we study the statistics of natural images in the Labelme data set. We not only confirm the well-known sparsity of image gradients, but also discover new joint behavior patterns of image gradients. Based on these statistical properties, we develop a sparse blind separation algorithm to estimate both layer motions and linear mixing coefficients and then recover all layers. This method can handle general parameterized motions, including translations, scalings, rotations, and other transformations. In addition, the number of layers is automatically identified, and all layers can be recovered, even in the underdetermined case where mixtures are fewer than layers. The effectiveness of this technology is shown in experiments on both simulated and real superimposed images.
我们解决了从线性混合、未知混合系数和未知层运动中分离多个源层的问题。当人们通过透明介质（如窗玻璃）拍照并且相机或介质在快照之间移动时，就会出现这种混合。为了了解如何实现正确的分离，我们研究了 Labelme 数据集中自然图像的统计信息。我们不仅证实了图像梯度的稀疏性是众所周知的，而且还发现了图像梯度的新的联合行为模式。基于这些统计特性，我们开发了一种稀疏盲分离算法来估计层运动和线性混合系数，然后恢复所有层。这种方法可以处理一般参数化运动，包括平移、缩放、旋转和其他变换。此外，还可以自动识别层的数量，并且即使在混合数量少于层的欠定情况下，也可以恢复所有层。该技术在模拟和真实叠加图像的实验中都证明了其有效性。
