Related papers: Random noise attenuation on finite-difference wave…
Existing diffusion-based purification methods aim to disrupt adversarial perturbations by introducing a certain amount of noise through a forward diffusion process, followed by a reverse process to recover clean examples. However, this…
We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the…
This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is…
Diffusion models (DMs) have recently emerged as SoTA tools for generative modeling in various domains. Standard DMs can be viewed as an instantiation of hierarchical variational autoencoders (VAEs) where the latent variables are inferred…
A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is…
Diffusion models have shown exceptional scaling properties in the image synthesis domain, and initial attempts have shown similar benefits for applying diffusion to unconditional text synthesis. Denoising diffusion models attempt to…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
Text-driven video generation has advanced significantly due to developments in diffusion models. Beyond the training and sampling phases, recent studies have investigated noise priors of diffusion models, as improved noise priors yield…
Progress in the development of coupled atomistic-continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic-continuum interface. This problem is mainly…
Noise shaping refers to an analog-to-digital conversion methodology in which quantization error is arranged to lie mostly outside the signal spectrum by means of oversampling and feedback. Recently it has been successfully applied to more…
Speech enhancement is designed to enhance the intelligibility and quality of speech across diverse noise conditions. Recently, diffusion model has gained lots of attention in speech enhancement area, achieving competitive results. Current…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
Quantum systems are inherently susceptible to noise -- a notorious factor that induces decoherence and limits the performance of quantum applications. To mitigate its detrimental effects, various techniques have been developed, including…
This paper addresses the problem of frequency-domain inter-carrier interference (ICI) mitigation for differential orthogonal frequency-division multiplexing (OFDM) systems. The classical fractional fast Fourier transform (F-FFT), adopting…
This paper proposes a new model based on Fuzzy k-Nearest Neighbors for classification with monotonic constraints, Monotonic Fuzzy k-NN (MonFkNN). Real-life data-sets often do not comply with monotonic constraints due to class noise. MonFkNN…
In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements, and specifically analyze the interaction between FRI techniques and the underlying sampling methods. We first obtain a…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
One of the fundamental challenges in image restoration is denoising, where the objective is to estimate the clean image from its noisy measurements. To tackle such an ill-posed inverse problem, the existing denoising approaches generally…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…