Related papers: Gaussian kernel smoothing
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
Recent efforts in using 3D Gaussians for scene reconstruction and novel view synthesis can achieve impressive results on curated benchmarks; however, images captured in real life are often blurry. In this work, we analyze the robustness of…
Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…
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…
Digital sensors can lead to noisy results under many circumstances. To be able to remove the undesired noise from images, proper noise modeling and an accurate noise parameter estimation is crucial. In this project, we use a…
In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due…
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…
Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…
We investigate the information on cosmology contained in Gaussianised weak gravitational lensing convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the…
A central goal of modern magnetic resonance imaging (MRI) is to reduce the time required to produce high-quality images. Efforts have included hardware and software innovations such as parallel imaging, compressed sensing, and deep…
Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where…
Implicit neural representations (INRs) have achieved remarkable success in image representation and compression, but they require substantial training time and memory. Meanwhile, recent 2D Gaussian Splatting (GS) methods (\textit{e.g.},…
Gaussian boson sampling (GBS) is a promising candidate for an experimental demonstration of quantum advantage using photons. However, sufficiently large noise might hinder a GBS implementation from entering the regime where quantum speedup…
Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second order differentiable. To tackle these three…
Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian…
When characterizing materials, it can be important to not only predict their mechanical properties, but also to estimate the probability distribution of these properties across a set of samples. Constitutive neural networks allow for the…
In various Computer Vision and Signal Processing applications, noise is typically perceived as a drawback of the image capturing system that ought to be removed. We, on the other hand, claim that image noise, just as texture, is important…
Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…
Bayesian optimization with Gaussian process as surrogate model has been successfully applied to analog circuit synthesis. In the traditional Gaussian process regression model, the kernel functions are defined explicitly. The computational…
Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…