Subspace Detection From Structured Union of Subspaces Via Linear Sampling

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Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of Compressive Sensing (CS), it is often assumed that the signal of interest is sparse in an orthonormal basis. However, in many practical applications, this requirement may be too restrictive. A generalization of the standard sparsity assumption is that the signal lies in a union of subspaces. Recovery of such signals from a small number of samples has been studied recently in several works. Here, the authors consider the problem of subspace detection in which their goal is to identify the subspace (from the union) in which the signal lies from a small number of samples, in the presence of noise.