A Hessian Schatten-Norm Regularization Approach For Solving Linear Inverse Problems
Stamatis Lefkimmiatis, EPFL STI LIB

Seminar • 20 February 2012

Abstract
In this presentation I will discuss about a class of convex non-quadratic regularizers that can be employed for solving ill-posed linear inverse imaging problems. These regularizers involve the Schatten norms of the Hessian matrix, which is computed at every pixel of the image, and they share many similarities with the total-variation (TV) semi-norm, in the sense that they both satisfy the same geometric invariance properties with respect to transformations of the coordinate system and they both depend on differential operators acting on the image. However, their advantage over TV is that by capturing second-order information of the image, they can deal more effectively with the well-known staircase effect, which is a common artifact met in TV-based reconstructions. Furthermore, a general first-order gradient-based optimization algorithm for the constrained minimization of the corresponding objective functions will be presented. The proposed algorithm is based on a primal-dual formulation and can efficiently cope with the non-smooth nature and the high-dimensionality of the problem under study.