Informative sensing of natural images

The theory of compressed sensing tells a dramatic story that sparse signals can be reconstructed near-perfectly from a small number of random measurements. However, recent work has found the story to be more complicated. For example, the projections based on principal component analysis work better than random projections for some images while the reverse is true for other images. Which feature of images makes such a distinction and what is the optimal set of projections for natural images? In this paper, we attempt to answer these questions with a novel formulation of compressed sensing. In particular, we find that bandwise random projections in which more projections are allocated to low spatial frequencies are near-optimal for natural images and demonstrate using experimental results that the bandwise random projections outperform other kinds of projections in image reconstruction.