The investigation of regularization schemes with sparsity promoting penalty terms has been
one of the dominant topics in the field of inverse problems over the last years, and Tikhonov …

Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

This book presents the state of the art in sparse and multiscale image and signal processing,
covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and …

This thoroughly updated new edition presents state of the art sparse and multiscale image
and signal processing. It covers linear multiscale geometric transforms, such as wavelet …

We consider the stable approximation of sparse solutions to nonlinear operator equations by
means of Tikhonov regularization with a subquadratic penalty term. Imposing certain …

This paper develops a novel sparse reconstruction algorithm for the electrical impedance
tomography problem of determining a conductivity parameter from boundary measurements …

The split feasibility problem (SFP) consists of finding a common point in the intersection of
finitely many convex sets, where some of the sets arise by imposing convex constraints in …

This paper addresses the regularization by sparsity constraints by means of weighted ℓ p
penalties for 0≤ p≤ 2. For 1≤ p≤ 2 special attention is payed to convergence rates in …

This paper deals with first-order numerical schemes for image restoration. These schemes
rely on a duality-based algorithm proposed in 1979 by Bermùdez and Moreno. This is an old …

This paper deals with the well-known discrepancy principle of Morozov. We show that the
principle can be used as an a posteriori choice rule for determining the regularization …