Matched subspace detection using compressively sampled data

We consider the problem of detecting whether a high dimensional signal lies in a given low dimensional subspace using only a few compressive measurements of it. By leveraging modern random matrix theory, we show that, even when we are short on information, a reliable detector can be constructed via a properly defined measure of energy of the signal outside the subspace. Our results extend those in [1] to a more general sampling framework. Moreover, the test statistic we define is much simpler than that required by [1], and it results in more efficient computation, which is crucial for high-dimensional data processing.