Related papers: Perturbation-Based Regularization for Signal Estim…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
The solution, $x$, of the linear system of equations $A x\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel $H(s,t)$ is considered. The Tikhonov regularized solution $ x(\lambda)$ is…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and…
Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…
In this work, we consider the problem of regularization in the design of minimum mean square error (MMSE) linear filters. Using the relationship with statistical machine learning methods, using a Bayesian approach, the regularization…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…
Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The $\ell_p$ norm covers a wide range of choices for the…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…
In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite element discretization of linear or nonlinear inverse…
This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…
In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…