  In "extreme" computational imaging that collects extremely undersampled or
noisy measurements, obtaining an accurate image within a reasonable computing
time is challenging. Incorporating image mapping convolutional neural networks
(CNN) into iterative image recovery has great potential to resolve this issue.
This paper 1) incorporates image mapping CNN using identical convolutional
kernels in both encoders and decoders into a block coordinate descent (BCD)
signal recovery method and 2) applies alternating direction method of
multipliers to train the aforementioned image mapping CNN. We refer to the
proposed recurrent network as BCD-Net using identical encoding-decoding CNN
structures. Numerical experiments show that, for a) denoising low
signal-to-noise-ratio images and b) extremely undersampled magnetic resonance
imaging, the proposed BCD-Net achieves significantly more accurate image
recovery, compared to BCD-Net using distinct encoding-decoding structures
and/or the conventional image recovery model using both wavelets and total
variation.
