Be'ery Efrat, Yeredor Arie
Department of Electrical Engineering-Systems, Tel-Aviv University, Tel-Aviv 69978 Isreal.
IEEE Trans Image Process. 2008 Mar;17(3):340-53. doi: 10.1109/TIP.2007.915548.
We consider the blind separation of source images from linear mixtures thereof, involving different relative spatial shifts of the sources in each mixture. Such mixtures can be caused, e.g., by the presence of a semi-reflective medium (such as a window glass) across a photographed scene, due to slight movements of the medium (or of the sources) between snapshots. Classical separation approaches assume either a static mixture model or a fully convolutive mixture model, which are, respectively, either under- or over-parameterized for this problem. In this paper, we develop a specially parameterized scheme for approximate joint diagonalization of estimated spectrum matrices, aimed at estimating the succinct set of mixture parameters: the static (gain) coefficients and the shift values. The estimated parameters are, in turn, used for convenient frequency-domain separation. As we demonstrate using both synthetic mixtures and real-life photographs, the advantage of the ability to incorporate spatial shifts is twofold: Not only does it enable separation when such shifts are present, but it also warrants deliberate introduction of such shifts as a simple source of added diversity whenever the static mixing coefficients form a singular matrix-thereby enabling separation in otherwise inseparable scenes.
我们考虑从源图像的线性混合中进行盲分离，其中每个混合中源存在不同的相对空间偏移。这种混合可能是由例如在拍摄场景中存在半反射介质（如窗户玻璃）引起的，这是由于在快照之间介质（或源）的轻微移动所致。经典的分离方法要么假设静态混合模型，要么假设完全卷积混合模型，对于这个问题，这两种模型分别参数化不足或过度。在本文中，我们开发了一种专门的参数化方案，用于对估计的频谱矩阵进行近似联合对角化，旨在估计混合参数的简洁集合：静态（增益）系数和偏移值。反过来，估计的参数用于方便的频域分离。正如我们使用合成混合和真实照片所展示的那样，纳入空间偏移能力的优势是双重的：它不仅在存在这种偏移时能够实现分离，而且当静态混合系数形成奇异矩阵时，它还保证可以有意引入这种偏移作为增加多样性的简单来源——从而在其他情况下不可分离的场景中实现分离。
