Compressed sensing mainly contains random projection and reconstruction. Because of lower convergence speed of iterative shrinkage algorithm and the lacking of direction of traditional 2-dimensional wavelet transform， random projection was implemented by using Permute Discrete Cosine Transform （PDCT）， and the gradient projection was used for reconstruction. Based on the simplification of computation complexity， the transformation coefficients in the dual-tree complex wavelet domain were improved by iteration. Finally， the reconstructed image was obtained by the inverse transform. In the experiments， the reconstruction results of DT CWT （Dual-Tree Complex Wavelet Transform） and bi-orthogonal wavelet were compared with the same reconstruction algorithm， and the former is better than the latter in image detail and smoothness with higher Peak Signal-to-Noise Ratio （PSNR） of 1.5 dB. In the same sparse domain， gradient projection converges faster than iterative shrinkage algorithm. And in the same sparse domain and random projection， PDCT has a slightly higher PSNR than the structural random matrix.