A Completion Network for Reconstruction from Compressed Acquisition

We consider here the problem of reconstructing an image from a few linear measurements. This problem has many biomedical applications, such as computerized tomography, magnetic resonance imaging and optical microscopy. While this problem has long been solved by compressed sensing methods, these are now outperformed by deep-learning approaches. However, understanding why a given network architecture works well is still an open question. In this study, we proposed to interpret the reconstruction problem as a Bayesian completion problem where the missing measurements are estimated from those acquired. From this point of view, a network emerges that includes a fully connected layer that provides the best linear completion scheme. This network has a lot fewer parameters to learn than direct networks, and it trains more rapidly than image-domain networks that correct pseudo inverse solutions. Although, this study focuses on computational optics, it might provide some insight for inverse problems that have similar formulations.