Date of Original Version
© 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Abstract or Description
We consider the problem of detecting whether a high dimensional vector ∈ ℝn lies in a r-dimensional subspace S, where r ≪ n, given few compressive measurements of the vector. This problem arises in several applications such as detecting anomalies, targets, interference and brain activations. In these applications, the object of interest is described by a large number of features and the ability to detect them using only linear combination of the features (without the need to measure, store or compute the entire feature vector) is desirable. We present a test statistic for subspace detection using compressive samples and demonstrate that the probability of error of the proposed detector decreases exponentially in the number of compressive samples, provided that the energy off the subspace scales as n. Using information-theoretic lower bounds, we demonstrate that no other detector can achieve the same probability of error for weaker signals. Simulation results also indicate that this scaling is near-optimal.
Proceedings of Statistical Signal Processing Workshop (SSP), 724-727.