Hessian Schatten-Norm Regularization for Linear Inverse Problems

Understand

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems.

• The proposed regularizers involve the Schatten norms of the Hessian matrix, computed at every pixel of the image.
• They can be viewed as second-order extensions of the popular total-variation (TV) semi-norm since they satisfy the same invariance properties.
• Meanwhile, by taking advantage of second-order derivatives, they avoid the staircase effect, a common artifact of TV-based reconstructions, and perform well for a wide range of applications.