Compressive imaging with complex wavelet transform and turbo AMP reconstruction

We extend the "turbo" belief propagation framework for compressive imaging to the dual-tree complex wavelet transform (DT-CWT) to exploit both sparsity and dependency across scales. Due to the near shift-invariance property and the improved angular resolution of DT-CWT, better reconstruction can be expected when incorporating with the compressed sensing (CS) algorithms. Two types priors to form the hidden Markov tree structure for the DT-CWT coefficients are con sidered. One models the real and imaginary components of DT-CWT separately while the other assumes the shared hid den states between the two. Simulations with natural images confirm an improved performance when iterating between the CS reconstruction and the DT-CWT HMT.