We propose a novel group regularization which we call exclusive lasso. Unlike the group lasso regularizer that assumes covarying variables in groups, the proposed exclusive lasso regularizer models the scenario when variables in the same group compete with each other. Analysis is presented to illustrate the properties of the proposed regularizer. We present a framework of kernel based multi-tas...

Statistical reconstruction methods for X-ray CT rely on regularization to yield good quality images. We propose and investigate a specific type of nonquadratic regularization for 3-D CT reconstruction that corresponds to applying a 2-D orthonormal wavelet transform (OWT) on trans-axial slices and finite differences (FD) along the axial direction. We use an iterative variable-splitting-based alt...

We propose to solve an image segmentation problem with connectivity constraints via projection onto the constraint set. The constraints form a convex set and the convex image segmentation problem with a total variation regularizer can be solved to global optimality in a primal-dual framework. Efficiency is achieved by directly computing the update of the primal variable via a projection onto th...

We propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total variation. One desira...

Nonlinear variational methods have become very powerful tools for many image processing tasks. Recently a new line of research has emerged, dealing with nonlinear eigenfunctions induced by convex functionals. This has provided new insights and better theoretical understanding of convex regularization and introduced new processing methods. However, the theory of nonlinear eigenvalue problems is ...

Abstract. We prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any smooth function Φ, we have that Φ(u) is TVD with the correct definition of the initial seminorm. We call this property Total Oscillation Diminishing. The reason being that it is in contradiction with the oscillations observed recently on some numeri...

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...

In this paper we provide a method to compute explicitly the solution of the total variation denoising problem with a L fidelity term, where p > 1, for piecewise constant data in dimension one.