Related papers: Bias-Reduction in Variational Regularization

Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this…

The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…

While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…

We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…

We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors' recent work on training feed-forward neural networks without the differentiation of activation functions. The…

Language models frequently inherit societal biases from their training data. Numerous techniques have been proposed to mitigate these biases during both the pre-training and fine-tuning stages. However, fine-tuning a pre-trained debiased…

We develop a new variational approach on level sets aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. With this new approach,…

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…

Gene expression analysis aims at identifying the genes able to accurately predict biological parameters like, for example, disease subtyping or progression. While accurate prediction can be achieved by means of many different techniques,…

Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…

In the past, optimization-based registration models have used spatially-varying regularization to account for deformation variations in different image regions. However, deep learning-based registration models have mostly relied on…

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning…

A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…