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We collect various facts related loosely to random Gaussian quadrilaterals in the plane. For example, a side of a degenerate quadrilateral (one point inside three others) has a density that is non-Rayleigh.
We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares…
The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
The extraction of spectral densities from Euclidean correlators evaluated on the lattice is an important problem, as these quantities encode physical information on scattering amplitudes, finite-volume spectra, inclusive decay rates, and…
Diffusion models (DMs) are generative models that learn to synthesize images from Gaussian noise. DMs can be trained to do a variety of tasks such as image generation and image super-resolution. Researchers have made significant…
Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
We use Bayesian inference and nested sampling to develop a non-parametric method to reconstruct the primordial power spectrum $P_{\mathcal{R}}(k)$ from Large Scale Structure (LSS) data. The performance of the method is studied by applying…
We study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem…
This paper presents a novel method for the reconstruction of images from samples located at non-integer positions, called mesh. This is a common scenario for many image processing applications, such as super-resolution, warping or virtual…
We investigate the gain in Shannon information that can be extracted from an X-ray image obtained after coherent free-space propagation of the transmitted beam and subsequent digital processing of the detected image. We show that simulated…
We revisit the issue of non-parametric gravitational lens reconstruction and present a new method to obtain the cluster mass distribution using strong lensing data without using any prior information on the underlying mass. The method…
We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
Depth cameras are an interesting modality for capturing vital signs such as respiratory rate. Plenty approaches exist to extract vital signs in a controlled setting, but in order to apply them more flexibly for example in multi-camera…
We present a novel Bayesian method for the joint reconstruction of cosmological matter density fields, peculiar velocities and power-spectra in the quasi-nonlinear regime. We study its applicability to the Ly-alpha forest based on multiple…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…