Related papers: Denoising Deterministic Time Series
This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then…
In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth $K$ in a metric space, but it got corrupted with noise so that some of the data points lie…
The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Data denoising is a persistent challenge across scientific and engineering domains. Real-world data is frequently corrupted by complex, non-linear noise, rendering traditional rule-based denoising methods inadequate. To overcome these…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Recent deep learning-based image denoising methods have shown impressive performance; however, many lack the flexibility to adjust the denoising strength based on the noise levels, camera settings, and user preferences. In this paper, we…
When taking photos under an environment with insufficient light, the exposure time and the sensor gain usually require to be carefully chosen to obtain images with satisfying visual quality. For example, the images with high ISO usually…
We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…
Experimental datasets are growing rapidly in size, scope, and detail, but the value of these datasets is limited by unwanted measurement noise. It is therefore tempting to apply analysis techniques that attempt to reduce noise and enhance…
It has been demonstrated that the amount of data is crucial in data-driven machine learning methods. Data is always valuable, but in some tasks, it is almost like gold. This occurs in engineering areas where data is scarce or very expensive…
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…
The lack of large-scale real raw image denoising dataset gives rise to challenges on synthesizing realistic raw image noise for training denoising models. However, the real raw image noise is contributed by many noise sources and varies…
We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible…
For the Nonlinear Shr\"odinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear…
Time series classification has received great attention over the past decade with a wide range of methods focusing on predictive performance by exploiting various types of temporal features. Nonetheless, little emphasis has been placed on…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances…
This work focuses on the regularization by nonlinear noise for a class of partial differential equations that may only have local solutions. In particular, we obtain the global existence, uniqueness and the Feller property for stochastic 3D…
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…