Compressive imaging via approximate message passing with wavelet-based image denoising

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over current state of the art compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose a compressive imaging algorithm that employs the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising of noisy signals. In this work, we apply an adaptive Wiener filter, which is a wavelet-based image denoiser, within AMP. Numerical results show that the proposed algorithm improves over the state of the art in both reconstruction error and runtime.