  Coded aperture is a promising approach for capturing the 4-D light field
(LF), in which the 4-D data are compressively modulated into 2-D coded
measurements that are further decoded by reconstruction algorithms. The
bottleneck lies in the reconstruction algorithms, resulting in rather limited
reconstruction quality. To tackle this challenge, we propose a novel
learning-based framework for the reconstruction of high-quality LFs from
acquisitions via learned coded apertures. The proposed method incorporates the
measurement observation into the deep learning framework elegantly to avoid
relying entirely on data-driven priors for LF reconstruction. Specifically, we
first formulate the compressive LF reconstruction as an inverse problem with an
implicit regularization term. Then, we construct the regularization term with
an efficient deep spatial-angular convolutional sub-network to comprehensively
explore the signal distribution free from the limited representation ability
and inefficiency of deterministic mathematical modeling. Experimental results
show that the reconstructed LFs not only achieve much higher PSNR/SSIM but also
preserve the LF parallax structure better, compared with state-of-the-art
methods on both real and synthetic LF benchmarks. In addition, experiments show
that our method is efficient and robust to noise, which is an essential
advantage for a real camera system. The code is publicly available at
\url{https://github.com/angmt2008/LFCA}
