Related papers: Sparse Bayesian mass-mapping with uncertainties: p…

Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining…

Weakly-Supervised Semantic Segmentation (WSSS) segments objects without a heavy burden of dense annotation. While as a price, generated pseudo-masks exist obvious noisy pixels, which result in sub-optimal segmentation models trained over…

We present a numerical investigation of nonlinear cluster lens reconstruction using weak lensing mass mapping. Recent advances in imaging and shear estimation have pushed reliable reduced shear measurements closer to cluster cores, making…

We consider the model {eqnarray*}y=X\theta^*+\xi, Z=X+\Xi,{eqnarray*} where the random vector $y\in\mathbb{R}^n$ and the random $n\times p$ matrix $Z$ are observed, the $n\times p$ matrix $X$ is unknown, $\Xi$ is an $n\times p$ random noise…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are…

Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…

The abundance of peaks in weak gravitational lensing maps is a potentially powerful cosmological tool, complementary to measurements of the shear power spectrum. We study peaks detected directly in shear maps, rather than convergence maps,…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and…

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…

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Current optical imaging surveys for cosmology are covering large areas of sky. To exploit the statistical power of these surveys for weak lensing measurements requires shape measurement methods with subpercent systematic errors. We…

In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…