Masking schemes for image manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the dimensions of the image space that preserves the manifold structure present in the original data. Such masking implements a form of compressed sensing that reduces power consumption in emerging imaging sensor platforms. Our goal is for the manifold learned from masked images to resemble the manifold learned from full images as closely as possible. We show that the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the manifolds learned from masked images resemble those learned from full images for modest mask sizes. Furthermore, our greedy algorithm performs similarly to the exhaustive search from integer programming at a fraction of the computational cost.