The invention provides two kinds of new compressive sensing technologies. In the first technical solution, there is proposed a permutation-based multi-dimensional sensing matrix and an iterative recovery algorithm with maximum likelihood (ML) local detection, which can fully exploit the digital nature of sparse signals. In the second technical solution, there is proposed a sparse measurement matrix which contains a permutation-based multi-dimensional measurement matrix, and an iterative recovery algorithm which fully utilizes the features of measurement symbols to design simple local recovery in each iteration. The second technical solution can achieve the linear decoding complexity and lower bound of sketch length empirically at the same time.