  How to construct a suitable measurement matrix is still an open question in
compressed sensing. A significant part of the recent work is that the
measurement matrices are not completely random on the entries but exhibit
considerable structure. In this paper, we proved that the symmetric Toeplitz
matrix and its transforms can be used as measurement matrix and recovery signal
with high probability. Compared with random matrices (e.g. Gaussian and
Bernullio matrices) and some structured matrices (e.g. Toeplitz and circulant
matrices), we need to generate fewer independent entries to obtain the
measurement matrix while the effectiveness of recovery does not get worse.
Furthermore, the signal can be recovered more efficiently by the algorithm.
