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Most existing image denoising algorithms can only deal with a single type of noise, which violates the fact that the noisy observed images in practice are often suffered from more than one type of noise during the process of acquisition and…
A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in non-null issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The…
The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational approach to…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…
We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated Gaussian random fields containing a number of pure white noise components. We propose a…
A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…
We introduce a two-round adaptive communication strategy that enables rate-optimal estimation in the white noise model without requiring prior knowledge of the underlying smoothness. In the first round, local machines send summary…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
Reliable state estimation hinges on accurate specification of sensor noise covariances, which weigh heterogeneous measurements. In practice, these covariances are difficult to identify due to environmental variability, front-end…
Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…
We consider a PDE approach to numerically solving the optimal transportation problem on the sphere. We focus on both the traditional squared geodesic cost and a logarithmic cost, which arises in the reflector antenna design problem. At each…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the…
In 2D acoustic and elastodynamic problems the spatial variability of a constitutive parameter such as the mass density makes it difficult to employ boundary integral and domain integral techniques to solve the forward and inverse wave…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…