Related papers: Wavelet-based density estimation for noise reducti…
From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. This…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
A wavelet-based changepoint method is proposed that determines when the variability of the noise in a sequence of functional profiles goes out-of-control from a known, fixed value. The functional portion of the profiles are allowed to come…
Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…
The effects of particle discreteness in N-body simulations of Lambda Cold Dark Matter (LambdaCDM) are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the…
Z pinches produce an X ray rich plasma environment where backlighting imaging of imploding targets can be quite challenging to analyze. What is required is a detailed understanding of the implosion dynamics by studying snapshot images of…
Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM). WaveDM learns the…
We present a new adaptive circuit simulation algorithm based on spline wavelets. The unknown voltages and currents are expanded into a wavelet representation, which is determined as solution of nonlinear equations derived from the circuit…
The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data…
Anomaly detection and localization in industrial images are essential for automated quality inspection. PaDiM, a prominent method, models the distribution of normal image features extracted by pre-trained Convolutional Neural Networks…
This paper focuses on the identification of the process noise density of a linear time-varying system described by the state-space model with the known measurement noise density. A novel method is proposed that enhances the measurement…
The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
The paper presents an image denoising algorithm by combining a method that is based on directional quasi-analytic wavelet packets (qWPs) with the popular BM3D algorithm. The qWPs and its corresponding transforms are designed in [1]. The…
Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure…