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Volumetric, multimodal imaging with precise spatial and temporal co-registration can provide valuable and complementary information for diagnosis and monitoring. Considerable research has sought to combine 3D photoacoustic (PA) and…

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

A polarimetric synthetic aperture radar (PolSAR) system, which uses multiple images acquired with different polarizations in both transmission and reception, has the potential to improve the description and interpretation of the observed…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…

Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…

Aims: Develop and validate tools to estimate residual noise covariance in Planck frequency maps. Quantify signal error effects and compare different techniques to produce low-resolution maps. Methods: We derive analytical estimates of…

The past few years have witnessed increasing research interest on covariance-based feature representation. A variety of methods have been proposed to boost its efficacy, with some recent ones resorting to nonlinear kernel technique. Noting…

We study how well the Gaussian approximation is valid for computing the covariance matrices of the convergence power and bispectrum in weak gravitational lensing analyses. We focus on its impact on the cosmological parameter estimations by…

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…

This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent,…

This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…

We adapt structural complexity analysis to three-dimensional signals, with an emphasis on brain magnetic resonance imaging (MRI). This framework captures the multiscale organization of volumetric data by coarse-graining the signal at…

We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first detecting occurrences, then…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…

Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections. They have achieved success in a multitude of applications such as neuroscience,…

Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…