Deep Learning and Inverse Problems
Ali Mohammad-Djafari Ning Chu Li Wang Liang Yu
Machine Learning (ML) methods and tools have gained great success in many
data, signal, image and video processing tasks, such as classification,
clustering, object detection, semantic segmentation, language processing,
Human-Machine interface, etc. In computer vision, image and video processing,
these methods are mainly based on Neural Networks (NN) and in particular
Convolutional NN (CNN), and more generally Deep NN. Inverse problems arise
anywhere we have indirect measurement. As, in general, those inverse problems
are ill-posed, to obtain satisfactory solutions for them needs prior
information. Different regularization methods have been proposed, where the
problem becomes the optimization of a criterion with a likelihood term and a
regularization term. The main difficulty, however, in great dimensional real
applications, remains the computational cost. Using NN, and in particular Deep
Learning (DL) surrogate models and approximate computation, can become very
helpful. In this work, we focus on NN and DL particularly adapted for inverse
problems. We consider two cases: First the case where the forward operator is
known and used as physics constraint, the second more general data driven DL
methods.