Related papers: Geometric kernel smoothing of tensor fields
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
In the previous paper [arXiv:2210.10435], the nonlinear perturbation theory of cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement…
Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…
We propose a bilateral filter with a locally controlled domain kernel for directional edge-preserving smoothing. Traditional bilateral filters use a range kernel, which is responsible for edge preservation, and a fixed domain kernel that…
We describe new methods for denoising and detection of gravitational waves embedded in additive Gaussian noise. The methods are based on Total Variation denoising algorithms. These algorithms, which do not need any a priori information…
In this paper we propose an efficient deep learning encoder-decoder network for performing Harmonic-Percussive Source Separation (HPSS). It is shown that we are able to greatly reduce the number of model trainable parameters by using a…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
Transmission electron microscope (TEM) images are often corrupted by noise, hindering their interpretation. To address this issue, we propose a deep learning-based approach using simulated images. Using density functional theory…
Deformation gradient tensor fields are reconstructed in three dimensions (mapping all 9 tensor components) using synthetic Dark-Field X-ray Microscopy data. Owing to the unique properties of the microscope, our results imply that the…
This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…
Time-of-Flight (ToF) sensors efficiently capture scene depth, but the nonlinear depth construction procedure often results in extremely large noise variance or even invalid areas. Recent methods based on deep neural networks (DNNs) achieve…
We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
This paper proposes a general decentralized framework for quantum kernel learning (QKL). It has robustness against quantum noise and can also be designed to defend adversarial information attacks forming a robust approach named RDQKL. We…