相关论文: Shannon wavelet approximations of linear different…
Starting from de la Vall\'ee Poussin type (VP) interpolation, the authors have recently introduced a family of interpolating polynomial scaling and wavelet bases generating the approximation and detail spaces of a non-standard…
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only…
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
The aim of this paper is to show the usefulness of Meyer wavelets for the classical problem of density estimation and for density deconvolution from noisy observations. By using such wavelets, the computation of the empirical wavelet…
A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approach exploits the local kernel theory which allows one to…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet data are discretized by nodal interpolation. As model…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…