  Compressed sensing (CS) is a challenging problem in image processing due to
reconstructing an almost complete image from a limited measurement. To achieve
fast and accurate CS reconstruction, we synthesize the advantages of two
well-known methods (neural network and optimization algorithm) to propose a
novel optimization inspired neural network which dubbed AMP-Net. AMP-Net
realizes the fusion of the Approximate Message Passing (AMP) algorithm and
neural network. All of its parameters are learned automatically. Furthermore,
we propose an AMPA-Net which uses three attention networks to improve the
representation ability of AMP-Net. Finally, We demonstrate the effectiveness of
AMP-Net and AMPA-Net on four standard CS reconstruction benchmark data sets.
Our code is available on https://github.com/puallee/AMPA-Net.
