Related papers: Stability of Image-Reconstruction Algorithms

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Image reconstruction enhanced by regularizers, e.g., to enforce sparsity, low rank or smoothness priors on images, has many successful applications in vision tasks such as computer photography, biomedical and spectral imaging. It has been…

Robustness is a fundamental property of machine learning classifiers required to achieve safety and reliability. In the field of adversarial robustness of image classifiers, robustness is commonly defined as the stability of a model to all…

We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the $n$-dimensional Heisenberg group into $CAT(0)$ spaces. Our main theorem establishes that these maps have the…

We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…

This report contains a numerical stability analysis of factorization algorithms for computing the Cholesky decomposition of symmetric positive definite matrices of displacement rank 2. The algorithms in the class can be expressed as…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e.g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine.…

We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…

In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we…

In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of $L^p(\Rd), 1\le p\le \infty$, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity.…

In this work, we establish regularity results for minimizers of the energy functional associated with the thin obstacle problem in Orlicz spaces. More precisely, we prove the Lipschitz continuity and the H\"older continuity of the gradient…

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…

Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct…

Deformable image registration is a fundamental task in medical image analysis and plays a crucial role in a wide range of clinical applications. Recently, deep learning-based approaches have been widely studied for deformable medical image…

In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is the Bessel potential operator ${\mathcal J}_\gamma,…

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…

Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…

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…