Is face recognition really a Compressive Sensing problem?

Compressive Sensing has become one of the standard methods of face recognition within the literature. We show, however, that the sparsity assumption which underpins much of this work is not supported by the data. This lack of sparsity in the data means that compressive sensing approach cannot be guaranteed to recover the exact signal, and therefore that sparse approximations may not deliver the robustness or performance desired. In this vein we show that a simple ℓ₂ approach to the face recognition problem is not only significantly more accurate than the state-of-the-art approach, it is also more robust, and much faster. These results are demonstrated on the publicly available YaleB and AR face datasets but have implications for the application of Compressive Sensing more broadly.