Related papers: Multiscale Methods for Shape Constraints in Deconv…
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the…
The problem of stationary robust L_infinity-induced deconvolution filtering for the uncertain continuous-time linear stochastic systems is addressed. The state space model of the system contains state- and input-dependent noise and…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
Deconvolution is the most widely used aberration correction technique in microscopy, however most techniques assume that the aberrations are the same for each point in the image, which is rarely true. Methods for tracking spatially varying…
The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
We consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input. From these observations, we wish to estimate the impulse responses of each of the…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
Depth completion, which aims to generate high-quality dense depth maps from sparse depth maps, has attracted increasing attention in recent years. Previous work usually employs RGB images as guidance, and introduces iterative spatial…
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process $M$ with intensity $n\to\infty$ as a model for a parent generation together with a Cox point process $N$ as offspring generation,…
Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…
Deconvolution of cell mixtures in "bulk" transcriptomic samples from homogenate human tissue is important for understanding the pathologies of diseases. However, several experimental and computational challenges remain in developing and…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…