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In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
The conventional way of formulating inverse problems such as identification of a (possibly infinite dimensional) parameter, is via some forward operator, which is the concatenation of the observation operator with the parameter-to-state-map…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent…
This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of…
We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for…
Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of properties of the subsurface which can be used to aid structural interpretation alongside the…