Abstract Systems biology is a new discipline built upon the premise that an understanding of
how cells and organisms carry out their functions cannot be gained by looking at cellular …

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 …

Recovering a function or high-dimensional parameter vector from indirect measurements is
a central task in various scientific areas. Several methods for solving such inverse problems …

Inverse problems arise from the need to interpret indirect and incomplete measurements. As
an area of contemporary mathematics, the field of inverse problems is strongly driven by …

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 …

The ill-posed problem of solving linear equations in the space of vector-valued finite Radon
measures with Hilbert space data is considered. Approximate solutions are obtained by …

Motivated by the theoretical and practical results in compressed sensing, efforts have been
undertaken by the inverse problems community to derive analogous results, for instance …

Optimization problems with convex but non-smooth cost functional subject to an elliptic
partial differential equation are considered. The non-smoothness arises from a L1-norm in …

This paper investigates the theoretical guarantees of ℓ^1-analysis regularization when
solving linear inverse problems. Most of previous works in the literature have mainly focused …

In this work, we consider the linear inverse problem $ y= Ax+\varepsilon $, where $ A\colon
X\to Y $ is a known linear operator between the separable Hilbert spaces $ X $ and $ Y …