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Positron emission tomography, like many other tomographic imaging modalities, relies on an image reconstruction step to produce cross-sectional images from projection data. Detection and localization of the back-to-back annihilation photons…
We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
The purpose of this study was to show how advanced concepts of compact, lossless and "Time Of Flight" (TOF) capable electronics similar to those foreseen for the LHC and ILC experiments could be fairly and easily transferred to the medical…
We developed a positron emission tomography (PET) system for multiple-isotope imaging. Our PET system, named multiple-isotope PET (MI-PET), can distinguish between different tracer nuclides using coincidence measurement of prompt…
Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns.…
Purpose: The scattering phenomenon creates degrading effects in positron emission tomography (PET) and the corresponding events are rejected conventionally. We have proposed a mathematical model to retrace the original line of response of…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a…
This work is the second part of a simulation study investigating the processing of densely packed and moving granular assemblies by positron emission particle tracking (PEPT). Since medical PET scanners commonly used for PEPT are very…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
Positron emission tomography (PET) is widely used in various clinical applications, including cancer diagnosis, heart disease and neuro disorders. The use of radioactive tracer in PET imaging raises concerns due to the risk of radiation…
This work aims at applying the theory of the component-based normalization for the Jagiellonian PET scanner, currently under development at the Jagiellonian University. In any Positron Emission Tomography acquisition, efficiency along a…
The aim of Electrical Impedance Tomography (EIT) is to determine the electrical conductivity distribution inside a domain by applying currents and measuring voltages on its boundary. Mathematically, the EIT reconstruction task can be…
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
This study presents a proof-of-concept for a novel Bayesian inverse method in a one-dimensional setting, aimed at proton beam therapy treatment verification. Our methodology is predicated on a hypothetical scenario wherein strategically…
Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence…