  Compressed sensing (CS) is a sampling theory that allows reconstruction of
sparse (or compressible) signals from an incomplete number of measurements,
using of a sensing mechanism implemented by an appropriate projection matrix.
The CS theory is based on random Gaussian projection matrices, which satisfy
recovery guarantees with high probability; however, sparse ternary {0, -1, +1}
projections are more suitable for hardware implementation. In this paper, we
present a deep learning approach to obtain very sparse ternary projections for
compressed sensing. Our deep learning architecture jointly learns a pair of a
projection matrix and a reconstruction operator in an end-to-end fashion. The
experimental results on real images demonstrate the effectiveness of the
proposed approach compared to state-of-the-art methods, with significant
advantage in terms of complexity.
