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We introduce the state-of-the-art deep learning Denoising Diffusion Probabilistic Model (DDPM) as a method to infer the volume or number density of giant molecular clouds (GMCs) from projected mass surface density maps. We adopt…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
Consider a reflected diffusion on the positive half-line. We approximate it by solutions of stochastic differential equations using the penalty method: We emulate the "hard barrier" of reflection by a "soft barrier" of a large drift…
In recent years, deep learning-based image compression, particularly through generative models, has emerged as a pivotal area of research. Despite significant advancements, challenges such as diminished sharpness and quality in…
Diffusion models have emerged as powerful priors for solving inverse problems in computed tomography (CT). In certain applications, such as neutron CT, it can be expensive to collect large amounts of measurements even for a single scan,…
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
Electron tomography is a technique used in both materials science and structural biology to image features well below optical resolution limit. In this work, we present a new algorithm for reconstructing the three-dimensional(3D)…
Traditional reconstruction-based methods have struggled to achieve competitive performance in anomaly detection. In this paper, we introduce Denoising Diffusion Anomaly Detection (DDAD), a novel denoising process for image reconstruction…
In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there…
Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…
Diffuse optical tomography (DOT) is an imaging modality which uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
Magnetic Resonance Imaging (MRI) is a powerful imaging technique widely used for visualizing structures within the human body and in other fields such as plant sciences. However, there is a demand to develop fast 3D-MRI reconstruction…
Anomaly detection has garnered extensive applications in real industrial manufacturing due to its remarkable effectiveness and efficiency. However, previous generative-based models have been limited by suboptimal reconstruction quality,…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted Magnetic Resonance Imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through…