Related papers: Geometric kernel smoothing of tensor fields
The presence of noise is common in signal processing regardless the signal type. Deep neural networks have shown good performance in noise removal, especially on the image domain. In this work, we consider deep neural networks as a…
Discretized techniques for vector tomographic reconstructions are prone to producing artifacts in the reconstructions. The quality of these reconstructions may further deteriorate as the amount of noise increases. In this work, we instead…
Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies of the…
Development of optical technology has enabled imaging of two-dimensional (2D) sound fields. This acousto-optic sensing enables understanding of the interaction between sound and objects such as reflection and diffraction. Moreover, it is…
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…
Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
For regression models, most of existing specification tests can be categorized into the class of local smoothing tests and of global smoothing tests. Compared with global smoothing tests, local smoothing tests can only detect local…
Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
We present a deep neural network to reduce coherent noise in three-dimensional quantitative phase imaging. Inspired by the cycle generative adversarial network, the denoising network was trained to learn a transform between two image…
The paper proposes a novel Kernelized image segmentation scheme for noisy images that utilizes the concept of Smallest Univalue Segment Assimilating Nucleus (SUSAN) and incorporates spatial constraints by computing circular colour map…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
It has been observed that even a small amount of noise introduced into the dataset can significantly degrade the performance of KAN. In this brief note, we aim to quantitatively evaluate the performance when noise is added to the dataset.…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
The FANOVA (or "Sobol'-Hoeffding") decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to…
We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…
This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional…