相关论文: Shearlet-based regularization in statistical inver…
The convergence rates results in $\ell^1$-regularization when the sparsity assumption is narrowly missed, presented by Burger et al. (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…
The $\ell_p$ regularization problem with $0< p< 1$ has been widely studied for finding sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. The proximal gradient…
In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals,…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
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…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
We introduce the concept of shape-regular regression maps as a framework to derive optimal rates of convergence for various non-parametric local regression estimators. Using Vapnik-Chervonenkis theory, we establish upper and lower bounds on…
In recent years, a series of convergence rates conditions for regularization methods has been developed. Mainly, the motivations for developing novel conditions came from the desire to carry over convergence rates results from the Hilbert…
Based on the powerful tool of variational inequalities, in recent papers convergence rates results on $\ell^1$-regularization for ill-posed inverse problems have been formulated in infinite dimensional spaces under the condition that the…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities,…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The…
In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…