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In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
In this paper, we present a novel approach to the estimation of strongly varying backgrounds in astronomical images by means of small objects removal and subsequent missing pixels interpolation. The method is based on the analysis of a…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
In this paper, we address the problem of global-scale image geolocation, proposing a mixed classification-retrieval scheme. Unlike other methods that strictly tackle the problem as a classification or retrieval task, we combine the two…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
Cross-resolution image alignment is a key problem in multiscale gigapixel photography, which requires to estimate homography matrix using images with large resolution gap. Existing deep homography methods concatenate the input images or…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Here, we address the problem of Independent Subspace Analysis (ISA). We develop a technique that (i) builds upon joint decorrelation for a set of functions, (ii) can be related to kernel based techniques, (iii) can be interpreted as a…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Due to strong learning abilities of convolutional neural networks (CNNs), they have become mainstream methods for image super-resolution. However, there are big differences of different deep learning methods with different types. There is…
Contrastive learning has revolutionized the field of computer vision, learning rich representations from unlabeled data, which generalize well to diverse vision tasks. Consequently, it has become increasingly important to explain these…
We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor's formula monomial basis. Error bounds for the…
Super-resolution is an important but difficult problem in image/video processing. If a video sequence or some training set other than the given low-resolution image is available, this kind of extra information can greatly aid in the…
Self-supervised methods have shown tremendous success in the field of computer vision, including applications in remote sensing and medical imaging. Most popular contrastive-loss based methods like SimCLR, MoCo, MoCo-v2 use multiple views…
Compared to widely used likelihood-based approaches, the minimum contrast (MC) method offers a computationally efficient method for estimation and inference of spatial point processes. These relative gains in computing time become more…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…