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To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
The success of many computer vision tasks lies in the ability to exploit the interdependency between different image modalities such as intensity and depth. Fusing corresponding information can be achieved on several levels, and one…
Recent progress in contrastive learning has revolutionized unsupervised representation learning. Concretely, multiple views (augmentations) from the same image are encouraged to map to the similar embeddings, while views from different…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
In the recent years, we witness a great interest in imaging, in a wide sense, using contrast agents. One of the reasons is that many imaging modalities, as the ones related to medical sciences, suffer from several shortcomings. The most…
Image warping is a necessary step in many multimedia applications such as texture mapping, image-based rendering, panorama stitching, image resizing and optical flow computation etc. Traditionally, color image warping interpolation is…
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for…
Semi-supervised learning (SSL) has long been proved to be an effective technique to construct powerful models with limited labels. In the existing literature, consistency regularization-based methods, which force the perturbed samples to…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
Pooling is a ubiquitous operation in image processing algorithms that allows for higher-level processes to collect relevant low-level features from a region of interest. Currently, max-pooling is one of the most commonly used operators in…
To calculate the intercept of the multigluon system in a symmetric spatial configuration a variational method is developed based on a complete system of one-gluon functions. The method is applied to two- and three- gluon cases to compare…
Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we…
We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the…
We implement an estimator for determining the separation between two incoherent point sources. This estimator relies on image inversion interferometry and when used with the appropriate data analytics, it yields an estimate of the…
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
Multimodal contrastive learning is a methodology for linking different data modalities; the canonical example is linking image and text data. The methodology is typically framed as the identification of a set of encoders, one for each…
We study hyperinterpolation and its spectral multiplier variants on the sphere under weak cubature assumptions formulated through Sobolev discrepancy estimates. In contrast with classical hyperinterpolation theory, our framework does not…