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The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…
In recent years, self-supervised denoising methods have gained significant success and become critically important in the field of image restoration. Among them, the blind spot network based methods are the most typical type and have…
Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
Music source separation (MSS) faces challenges due to the limited availability of correctly-labeled individual instrument tracks. With the push to acquire larger datasets to improve MSS performance, the inevitability of encountering…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
We introduce a novel method that we call Single-Shot Cross-Spectroscopy (SSCS), for extracting the auto- and cross-power spectral densities of dephasing noise of a qubit pair. The method uses straightforward input, namely single-shot…
In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution,…
In real-world scenarios, collected and annotated data often exhibit the characteristics of multiple classes and long-tailed distribution. Additionally, label noise is inevitable in large-scale annotations and hinders the applications of…
We propose a novel, good-quality, and less demanding method for detecting knots on the surface of wooden logs using multimodal data fusion. Knots are a primary factor affecting the quality of sawn timber, making their detection fundamental…
In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
Noisy images processing is a fundamental task of computer vision. The first example is the detection of faint edges in noisy images, a challenging problem studied in the last decades. A recent study introduced a fast method to detect faint…
Speckle noise is a fundamental challenge in coherent imaging systems, significantly degrading image quality. Over the past decades, numerous despeckling algorithms have been developed for applications such as Synthetic Aperture Radar (SAR)…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
Optical coherence tomography (OCT) is a prevalent imaging technique for retina. However, it is affected by multiplicative speckle noise that can degrade the visibility of essential anatomical structures, including blood vessels and tissue…
We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…
Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…
We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the…