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Source Separation with Side Information Based on Gaussian Mixture Models With Application in Art Investigation
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.2964195
Zahra Sabetsarvestani , Francesco Renna , Franz Kiraly , Miguel Rodrigues

In this paper, we propose an algorithm for source separation with side information where one observes the linear superposition of two source signals plus two additional signals that are correlated with the mixed ones. Our algorithm is based on two ingredients: first, we learn a Gaussian mixture model (GMM) for the joint distribution of a source signal and the corresponding correlated side information signal; second, we separate the signals using standard computationally efficient conditional mean estimators. The paper also puts forth new recovery guarantees for this source separation algorithm. In particular, under the assumption that the signals can be perfectly described by a GMM model, we characterize necessary and sufficient conditions for reliable source separation in the asymptotic regime of low-noise as a function of the geometry of the underlying signals and their interaction. It is shown that if the subspaces spanned by the innovation components of the source signals with respect to the side information signals have zero intersection, provided that we observe a certain number of linear measurements from the mixture, then we can reliably separate the sources; otherwise we cannot. Our proposed framework – which provides a new way to incorporate side information to aid the solution of source separation problems where the decoder has access to linear projections of superimposed sources and side information – is also employed in a real-world art investigation application involving the separation of mixtures of X-ray images. The simulation results showcase the superiority of our algorithm against other state-of-the-art algorithms.

中文翻译:

基于高斯混合模型的边信息源分离在艺术调查中的应用

在本文中,我们提出了一种带有边信息的源分离算法,其中观察两个源信号加上与混合信号相关的两个附加信号的线性叠加。我们的算法基于两个要素:首先,我们学习高斯混合模型 (GMM),用于源信号和相应的相关边信息信号的联合分布;其次,我们使用标准的计算高效的条件均值估计器来分离信号。论文还对该源分离算法提出了新的恢复保证。特别是在假设信号可以被 GMM 模型完美描述的情况下,我们将在低噪声渐近状态下可靠源分离的必要和充分条件表征为基础信号几何形状及其相互作用的函数。结果表明,如果源信号的创新分量相对于边信息信号所跨越的子空间具有零交集,只要我们从混合中观察到一定数量的线性测量,那么我们就可以可靠地分离源;否则我们不能。我们提出的框架——它提供了一种新的方法来合并辅助信息以帮助解决源分离问题,其中解码器可以访问叠加源和辅助信息的线性投影——也被用于涉及分离的现实世界艺术调查应用程序X 射线图像的混合。
更新日期:2020-01-01
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