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The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current…

The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…

This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…

The spectrogram is a classical DSP tool used to view signals in both time and frequency. Unfortunately, the Heisenberg Uncertainty Principal limits our ability to use them for detecting and measuring narrowband signal modulation in wideband…

Increased use of sensor signals from wearable devices as rich sources of physiological data has sparked growing interest in developing health monitoring systems to identify changes in an individual's health profile. Indeed, machine learning…

The detection of signals hidden in noise is one of the oldest and common problems in astronomy. Various solutions have been proposed in the past such as the parametric approaches based on the least-squares fit of theoretical templates or…

Many commercial and defense applications involve multisensor, multitarget tracking, requiring the fusion of information from a set of sensors. An interesting use case occurs when data available at a central node (due to geometric diversity…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

Diffusion models have achieved impressive results in generating high-quality images. Yet, they often struggle to faithfully align the generated images with the input prompts. This limitation is associated with synchronous denoising, where…

Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…

In recent years the possibility of measuring the temporal change of radial and transverse position of sources in the sky in real time have become conceivable thanks to the thoroughly improved technique applied to new astrometric and…

The first step when investigating time varying data is the detection of any reliable changes in star brightness. This step is crucial to decreasing the processing time by reducing the number of sources processed in later, slower steps.…

Sensors measuring real-life physical processes are ubiquitous in today's interconnected world. These sensors inherently bear noise that often adversely affects performance and reliability of the systems they support. Classic filtering-based…

We apply a Machine Learning technique known as Convolutional Denoising Autoencoder to denoise synthetic images of state-of-the-art radio telescopes, with the goal of detecting the faint, diffused radio sources predicted to characterise the…

State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…

Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are…

The detection limit of astronomical imaging observations is limited by several noise sources. Some of that noise is correlated between neighbouring image pixels and exposures, so in principle could be learned and corrected. We present an…

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary…

Image denoising based on deep learning has witnessed significant advancements in recent years. However, existing deep learning methods lack quantitative control of the deviation or error on denoised images. The neural networks Self2Self is…

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time…