Super-resolution with adaptive regularization

Multi-channel super-resolution is a means of recovering high frequency information by trading off the temporal bandwidth. Almost all the methods proposed in the literature are based on optimizing a cost function. But since the problem is usually ill-posed, one needs to impose some regularity constraints. However, regularity constraints tend to attenuate the high frequency contents of the data (usually present in the form of discontinuities). This inherent contradiction between regularization and super-resolution has not been addressed in the literature, despite the availability of off the shelf tools. W have investigated this issue in the context of adaptive regularization, using φ-functions (convex, non-convex, bounded, unbounded)