  Compressed sensing is a promising technique that attempts to faithfully
recover sparse signal with as few linear and nonadaptive measurements as
possible. Its performance is largely determined by the characteristic of
sensing matrix. Recently several zero-one binary sensing matrices have been
deterministically constructed for their relative low complexity and competitive
performance. Considering the complexity of implementation, it is of great
practical interest if one could further improve the sparsity of binary matrix
without performance loss. Based on the study of restricted isometry property
(RIP), this paper proposes the near-optimal binary sensing matrix, which
guarantees nearly the best performance with as sparse distribution as possible.
The proposed near-optimal binary matrix can be deterministically constructed
with progressive edge-growth (PEG) algorithm. Its performance is confirmed with
extensive simulations.
