分析与结构综合--关于图的子空间模型并的研究
Analysis vs Synthesis with Structure - An Investigation of Union of Subspace Models on Graphs
摘要：
我们考虑的问题，表征稀疏合成和cosparse分析驱动的信号模型之间的“二元性差距”，通过镜头的谱图理论，在努力理解它们的精确的等价性和差异。通过检测和利用固有的连接结构，因此，不同的一组属性，秩亏图差分矩阵，如图拉普拉斯算子，我们能够证实cosparse分析和稀疏合成模型之间的差异，根据前者构成了后者的约束和翻译的实例。针对一般的子空间并集模型，研究了关联子空间及其组成，进一步细化了特殊的唯一性和恢复保证，并基于图关联矩阵发现了一个底层的结构稀疏模型.此外，对于循环图，我们提供了一个确切的特征的基础子空间，推导出封闭形式的表达式，以及证明之间的过渡性质等价和非等价的参数推广的图形拉普拉斯算子。
英文摘要：
We consider the problem of characterizing the `duality gap' between sparse synthesis- and cosparse analysis-driven signal models through the lens of spectral graph theory, in an effort to comprehend their precise equivalencies and discrepancies. By detecting and exploiting the inherent connectivity structure, and hence, distinct set of properties, of rank-deficient graph difference matrices such as the graph Laplacian, we are able to substantiate discrepancies between the cosparse analysis and sparse synthesis models, according to which the former constitutes a constrained and translated instance of the latter. In view of a general union of subspaces model, we conduct a study of the associated subspaces and their composition, which further facilitates the refinement of specialized uniqueness and recovery guarantees, and discover an underlying structured sparsity model based on the graph incidence matrix. Furthermore, for circulant graphs, we provide an exact characterization of underlying subspaces by deriving closed-form expressions as well as demonstrating transitional properties between equivalence and non-equivalence for a parametric generalization of the graph Laplacian.
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