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Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and…
Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source…
Photocount statistics are an important tool for the characterization of electromagnetic fields, especially for fields with an irrelevant phase. In the microwave domain, continuous rather than discrete measurements are the norm. Using a…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is…
In recent years, the cross spectrum has received considerable attention as a means of characterising the variability of astronomical sources as a function of wavelength. While much has been written about the statistics of time and phase…
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…
The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…
The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed…
Photoacoustic spectral analysis is a novel tool for studying various parameters affecting signals in Photoacoustic microscopy. But only observing frequency components of photoacoustic signals doesn't make enough data for a desirable…
The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…
Spectrograms visualize the frequency components of a given signal which may be an audio signal or even a time-series signal. Audio signals have higher sampling rate and high variability of frequency with time. Spectrograms can capture such…
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
In this work we demonstrate the use of neural networks for rapid extraction of signal parameters of discretely sampled signals. In particular, we use dense autoencoder networks to extract the parameters of interest from exponentially…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…