Related papers: Geometric kernel smoothing of tensor fields
We prove solenoidal injectivity for the geodesic X-ray transform of tensor fields on simple Riemannian manifolds with $C^{1,1}$ metrics and non-positive sectional curvature. The proof of the result rests on Pestov energy estimates for a…
Noise and decoherence due to spurious two-level systems (TLS) located at material interfaces is a long-standing issue in solid state quantum technologies. Efforts to mitigate the effects of TLS have been hampered by a lack of surface…
Mesh denoising is a fundamental problem in digital geometry processing. It seeks to remove surface noise, while preserving surface intrinsic signals as accurately as possible. While the traditional wisdom has been built upon specialized…
The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…
Seismic denoising is an important processing step before subsequent imaging and interpretation, which consumes a significant amount of time, whether it is for Quality control or for the associated computations. We present results of our…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic…
We study breaking stress of deformed Coulomb crystals in a neutron star crust, taking into account electron plasma screening of ion-ion interaction; calculated breaking stress is fitted as a function of electron screening parameter. We…
The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To…
We study some properties of smoothing kernels and their local expression as they appear in the construction of Colombeau-type generalized function algebras which are diffeomorphism invariant.
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
Nuclear Magnetic Resonance (NMR) spectroscopy is an important analytical tool in chemistry, biology, and life science, but it suffers from relatively low sensitivity and long acquisition time. Thus, improving the apparent signal-to-noise…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
Seismologists often need to gather information about the subsurface structure of a location to determine if it is fit to be drilled for oil. However, there may be electrical noise in seismic data which is often removed by disregarding…
Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…
In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…
Diffusion is a prominent source of noise affecting nuclear magnetic resonance at the nanometer scale (nano-NMR), preventing high resolution studies of unpolarized liquid samples. Actively managing diffusion noise through, for example,…
Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…