  Regularization plays a crucial role in reliably utilizing imaging systems for
scientific and medical investigations. It helps to stabilize the process of
computationally undoing any degradation caused by physical limitations of the
imaging process. In the past decades, total variation regularization,
especially second-order total variation (TV-2) regularization played a dominant
role in the literature. Two forms of generalizations, namely Hessian-Schatten
norm (HSN) regularization, and total generalized variation (TGV)
regularization, have been recently proposed and have become significant
developments in the area of regularization for imaging inverse problems owing
to their performance. Here, we develop a novel regularization for image
recovery that combines the strengths of these well-known forms. We achieve this
by restricting the maximization space in the dual form of HSN in the same way
that TGV is obtained from TV-2. We name the new regularization as the
generalized Hessian-Schatten norm regularization (GHSN), and we develop a novel
optimization method for image reconstruction using the new form of
regularization based on the well-known framework called alternating direction
method of multipliers (ADMM). We demonstrate the strength of the GHSN using
some reconstruction examples.
