Minimax sparse detection based on one-class classifiers

We consider the problem of detecting a target signature which is known (up to an amplitude factor) to belong to a (possibly very) large library of signatures. Thus we know how each signature to be detected looks like, but we do not know which one is activated under H₁. We propose a minimax approach for this problem aimed at maximizing the worst detection performance. Optimization issues and connections with One-Class classifiers are discussed and illustrated geometrically. Numerical results comparing the proposed approach to the classical sparse-coding dictionary learning technique K-SVD are provided on astrophysical hyperspectral data.