一种结构矩阵分解的通有唯一性及其在盲源分离中的应用
Generic uniqueness of a structured matrix factorization and applications in blind source separation
摘要：
代数几何，虽然很少探索信号处理，提供了工具，是非常方便的调查在广泛的应用中的一般属性。泛型属性是“几乎处处“都存在的属性。我们提出了一组条件，足以证明某种结构矩阵分解的通用唯一性。这组条件可以用作不同设置中通用唯一性的检查表。我们将详细讨论两个特定的应用程序。我们提供了一个宽松的通用唯一性条件联合矩阵对角化，是相关的独立分量分析在欠定的情况下。我们提出了通用的唯一性条件，最近提出的一类确定性盲源分离方法，依赖于温和的源模型。对于感兴趣的读者，我们提供了一些直观的结果是如何连接到他们的代数几何根。
英文摘要：
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost everywhere". We present a set of conditions that are sufficient for demonstrating the generic uniqueness of a certain structured matrix factorization. This set of conditions may be used as a checklist for generic uniqueness in different settings. We discuss two particular applications in detail. We provide a relaxed generic uniqueness condition for joint matrix diagonalization that is relevant for independent component analysis in the underdetermined case. We present generic uniqueness conditions for a recently proposed class of deterministic blind source separation methods that rely on mild source models. For the interested reader we provide some intuition on how the results are connected to their algebraic geometric roots.
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