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Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scaterrers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all…
Traditional Phase-Linking (PL) algorithms are known for their high cost, especially with the huge volume of Synthetic Aperture Radar (SAR) images generated by Sentinel-1 SAR missions. Recently, a COvariance Fitting Interferometric Phase…
Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…
We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These models are motivated by multi-modal learning and form the…
A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of state with different total number of particles,…
The Period-Luminosity (PL) relation is usually derived using time-averaged magnitudes, which require multiple-epoch observations to determine periods and adequately sample the light curves. Although single-epoch observations are more…
Recently, the Hilbert-Schmidt speed, as a special class of quantum statistical speed, has been reported to improve the interferometric phase in single-parameter quantum estimation. Here, we test this concept in the multiparameter scenario…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
The phase locking value (PLV) is a widely used measure to detect phase connectivity. Main drawbacks of the standard PLV are it can be sensitive to noisy observations and does not provide uncertainty measures under finite samples. To…
Quantum coherence is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce…
Aims. We aim at creating a Bayesian model to infer the coefficients of PL or PLZ relations that propagates uncertainties in the observables in a rigorous and well founded way. Methods. We propose a directed acyclic graph to encode the…
Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $\alpha$-affinity, say $\alpha$-affinity of coherence for $\alpha \in (0, 1)$.…
Standard methods, such as sequential procedures based on Johansen's (pseudo-)likelihood ratio (PLR) test, for determining the co-integration rank of a vector autoregressive (VAR) system of variables integrated of order one can be…
Precise measurements in optical and atomic systems often rely on differential interferometry. This method allows to handle large and correlated phase noise contributions -- such as environmental vibrations, thermal fluctuations, or…
The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases.…
Interferometric measurements of high-harmonics induced by multiple laser fields in an emerging field of research that promises optimized yield of harmonics, and time and space-resolved nonlinear spectroscopy. Most of the measurements have…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…