Ensuring measurement consistency in deep learning methods for linear inverse problems

The best performing methods for solving linear inverse problems are based on deep learning. These have been applied to various image restoration tasks such as inpainting and denoising as well as for reconstructing MR and CT images. In these tasks, deep networks are trained to find the inverse of the forward operation by learning the map between the measurements and the input images. This setting results in measurement inconsistency and becomes problematic in critical domains such as medical imaging. To address this problem, a framework that integrates optimisation and deep learning methods is proposed, which ensures that deep network outputs are more reliable.