Deep learning methods for solving linear inverse problems: Research directions and paradigms

Deep Learning for Linear Inverse Problems Using the Plug-and-Play Priors Framework

“…1. The decomposition of the error in the solution of linear inverse problems [1]. observed data is often corrupted by some noise n ∈ R M , i.e., y = Ax + n, (2) so that the recovery of the vector of interest from the observation vector is only possible subject to some approximation.…”

“…As a long-standing problem, a number of algorithms have been proposed in literature to solve linear inverse problems. There are two broad classes of approaches to tackle inverse problems, i.e., model based approaches and learning based approaches [1,2]. Model-based approaches leverage knowledge of the underlying linear model to solve inverse problems via the formulation of optimization problems that include two terms in the objective: (1) a data fidelity term and (2) a data regularization.…”

“…Alternatively, learning based approaches leverage the rapid development of deep learning (DL) techniques in recent years to tackle inverse problems [1,2,3]. For example, by unfolding an iterative algorithm into a neural network, we can learn the parameters of resulting neural network from training data [4,5].…”

“…The linear inverse problem arises in various scientific areas such as astronomy, remote sensing, medical imaging, and telecommunications to name a few [1]. In recent years, innumerable attempts have been carried out to solve different variants of the linear inverse problems -such as the sparse linear inverse problem and the low-rank linear inverse problem -in different applications [1].…”

AI assisted PHY in future wireless systems: Recent developments and challenges

“…For complex communications scenarios that are difficult to describe with concrete mathematical models, AI could be a potential solution in order to provide promising new benefits. In addition, AI has been proved be a powerful tool in solving linear inverse problems [2].…”