The characteristic of different chaotic sequences for Compressive Sensing

Compressive Sensing (CS) is a new sampling theory which captures signals at sub-Nyquist rate without jeopardizing signal recovery. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. Generally, this kind of matrix is constructed by the Gaussian random matrix or Bernoulli random matrix. In this work, we systematically investigate the possibility of constructing measurement matrices with different chaotic sequences. With these matrices, we apply them in compressive sensing of digital images and compare the accuracy of reconstruction while using each of them to construct measurement matrices. Experimental results show that the matrices constructed by chaotic sequences can be sufficient to satisfy RIP with high probability and suitable to construct measurement matrices, whose characteristics can really outperform Gaussian random matrix. Meanwhile, the performances of the different chaotic sensing matrices are almost equal and most of them are superior to Gaussian random matrix for some compression ratio.