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Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
In a great number of tasks in science and engineering, the goal is to infer an unknown image from a small number of measurements collected from a known forward model describing certain sensing or imaging modality. Due to resource…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most…
This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…
We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey…
The new generation of radio telescopes, such as the Square Kilometer Array (SKA), requires dramatic advances in computer hardware and software, in order to process the large amounts of produced data efficiently. In this document, we explore…
High fidelity radio interferometric data calibration that minimises spurious spectral structure in the calibrated data is essential in astrophysical applications, such as 21 cm cosmology, which rely on knowledge of the relative spectral…
Forward modeling of wave scattering and radar imaging mechanisms is the key to information extraction from synthetic aperture radar (SAR) images. Like inverse graphics in optical domain, an inherently-integrated forward-inverse approach…
Detection of B-mode polarization of the cosmic microwave background (CMB) radiation is one of the frontiers of observational cosmology. Because they are an order of magnitude fainter than E-modes, it is quite a challenge to detect B-modes.…
We are interested in creating an automated or semi-automated system with the capability of taking a set of radar imagery, collection parameters and a priori map and other tactical data, and producing likely interpretations of the possible…
In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process.…
We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with…
We present a proof-of-concept analysis of photometric redshifts with Bayesian priors on physical properties of galaxies. This concept is particularly suited for upcoming/on-going large imaging surveys, in which only several broad-band…
The image acquisition parameters (IAPs) used to create MRI scans are central to defining the appearance of the images. Deep learning models trained on data acquired using certain parameters might not generalize well to images acquired with…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
In this paper we introduce a reliable, fully automated and fast algorithm to detect extended extragalactic radio sources (cluster of galaxies, filaments) in existing and forthcoming surveys (like LOFAR and SKA). The proposed solution is…
The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging including magnetic resonance imaging (MRI).…