Related papers: Regularization Graphs -- A unified framework for v…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…
Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
Regularization is commonly used for alleviating overfitting in machine learning. For convolutional neural networks (CNNs), regularization methods, such as DropBlock and Shake-Shake, have illustrated the improvement in the generalization…
Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models. In many cases these parameter fields reflect different attributes of a single…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…