Related papers: Geometric kernel smoothing of tensor fields
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary…
A structure-preserving kernel ridge regression method is presented that allows the recovery of globally defined, potentially high-dimensional, and nonlinear Hamiltonian functions on Poisson manifolds out of datasets made of noisy…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we…
High resolution dark matter only simulations provide a realistic and fully general means to study the theoretical predictions of cosmological structure formation models for gravitational lensing. Due to the finite number of particles, the…
A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus…
A method for estimating the incident sound field inside a region containing scattering objects is proposed. The sound field estimation method has various applications, such as spatial audio capturing and spatial active noise control;…
Linear perturbation is used to investigate the effect of gravitational softening on the retrieved two-armed spiral eigenmodes of razor-thin stellar discs. We explore four softening kernels with different degrees of gravity bias, and…
During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal…
Removing the shape noise from the observed weak lensing field, i.e., denoising, enhances the potential of WL by accessing information at small scales where the shape noise dominates without denoising. We utilise two machine learning (ML)…
The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a…
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…
The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation…
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…
Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits…
The geodesic ray-tracing method has shown its effectiveness for the reconstruction of fibers in white matter structure. Based on reasonable metrics on the spaces of the diffusion tensors, it can provide multiple solutions and get robust to…