Related papers: Uniqueness theorem for analytic functions and its …
Noisy images are a challenge to image compression algorithms due to the inherent difficulty of compressing noise. As noise cannot easily be discerned from image details, such as high-frequency signals, its presence leads to extra bits…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach…
We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigroups in Banach spaces with Fourier type.
For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha+\gamma>1$, where $\gamma$ denotes the Holder index of the drift coefficient. We prove existence…
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths and…
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are closely related, yet there is limited work in exploring this…
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…
This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition…
Score matching enables the estimation of the gradient of a data distribution, a key component in denoising diffusion models used to recover clean data from corrupted inputs. In prior work, a heuristic weighting function has been used for…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
Anonymized data is highly valuable to both businesses and researchers. A large body of research has however shown the strong limits of the de-identification release-and-forget model, where data is anonymized and shared. This has led to the…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
Noisy labelled datasets are generally inexpensive compared to clean labelled datasets, and the same is true for graph data. In this paper, we propose a denoising technique DeGLIF: Denoising Graph Data using Leave-One-Out Influence Function.…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
Mismatching problem between the source and target noisy corpora severely hinder the practical use of the machine-learning-based voice activity detection (VAD). In this paper, we try to address this problem in the transfer learning…
Image denoising is a fundamental task in computer vision. While prevailing deep learning-based supervised and self-supervised methods have excelled in eliminating in-distribution noise, their susceptibility to out-of-distribution (OOD)…
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of…