Related papers: A unifying representer theorem for inverse problem…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
Statistical inverse learning theory, a field that lies at the intersection of inverse problems and statistical learning, has lately gained more and more attention. In an effort to steer this interplay more towards the variational…
A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
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…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
For a Hilbert space setting Chambolle and Pock introduced an attractive first-order algorithm which solves a convex optimization problem and its Fenchel dual simultaneously. We present a generalization of this algorithm to Banach spaces.…
This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…
Bayesian regularization is a central tool in modern-day statistical and machine learning methods. Many applications involve high-dimensional sparse signal recovery problems. The goal of our paper is to provide a review of the literature on…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…
Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
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…