Related papers: Variably Scaled Kernels for the regularized soluti…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
Almost every single image restoration problem has a closely related parameter, such as the scale factor in super-resolution, the noise level in image denoising, and the quality factor in JPEG deblocking. Although recent studies on image…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes…
For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Separable nonlinear least squares problems appear in many inverse problems, including semi-blind image deblurring. The variable projection (VarPro) method provides an efficient approach for solving such problems by eliminating linear…
A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. It is…
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…
Deep Learning-based Computer Vision field has recently been trying to explore larger kernels for convolution to effectively scale up Convolutional Neural Networks. Simultaneously, new paradigm of models such as Vision Transformers find it…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…
One of the most important issues in the image processing is the approximation of the image that has been lost due to the blurring process. These types of matters are divided into non-blind and blind problems. The second type of problem is…
Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing…