Related papers: Mathematical Challenges Arising in Thermoacoustic …
Medical imaging modalities have revolutionized health-care approaches by offering a better understanding of the human anatomy. Discovery of x-rays allowed the exploiting of the micro-scaled information of human anatomy. Computed tomography…
A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
Over the past decades, thermal ablation procedures such as high intensity focused ultrasound (HIFU) have been developed vaporize cancerous tissues in a focal area. Thermal ablation has the potential to non-invasively eliminate tumors and…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
Simulation involves predicting responses of a physical system. In this article, we simulate opto-acoustic signals generated in a three-dimensional volume due to absorption of an optical pulse. A separable computational model is developed…
This work builds on the previous introduction [1] of a coupled experimental-computational system devised to fully characterize the thermal behavior of complex 3D submicron electronic devices. The new system replaces the laser-based surface…
In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In Part I, we establish Carleman estimates for the coupled quantitative thermoacoustic equations by assuming that the…
Purpose: Photoacoustic tomography (PAT) is a novel imaging technique that can spatially resolve both morphological and functional tissue properties, such as the vessel topology and tissue oxygenation. While this capacity makes PAT a…
We consider the problem of thermoacoustic tomography (TAT), in which one needs to reconstruct the initial value of a solution of the wave equation from its value on an observation surface. We show that if some geometric rays for the…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic…
Predictions of thermoacoustic instabilities in annular combustors are essential but difficult. Axial variations of flow and thermal parameters increase the cost of numerical simulations and restrict the application of analytical solutions.…
Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be…
Diffusion models have recently emerged as powerful priors for solving inverse problems. While computed tomography (CT) is theoretically a linear inverse problem, it poses many practical challenges. These include correlated noise, artifact…
Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…
Speeding up the data acquisition is one of the central aims to advance tomographic imaging. On the one hand, this reduces motion artifacts due to undesired movements, and on the other hand this decreases the examination time for the…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…