Benjamin Palacios

Benjamin Palacios
University of Chicago | UC · Department of Statistics

Ph.D. in Mathematics, University of Washington
Assistant Professor, Department of Mathematics, Universidad Católica de Chile.

About

14
Publications
691
Reads
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62
Citations
Citations since 2017
11 Research Items
61 Citations
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2017201820192020202120222023051015
2017201820192020202120222023051015

Publications

Publications (14)
Article
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and some advances have been made on the topic. In particular, stability inequalities have been proposed for the i...
Preprint
This paper concerns the reconstruction of properties of narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements, based on light detection away from the main path of the beam. We first model light propagation in the beam itself by macroscopic approximations of radiative transfer equations that take t...
Preprint
Full-text available
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and some advances have been made on the topic. In particular, stability inequalities have been proposed for the i...
Article
We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations by fractional Fermi pencil beam models. We obtain an error estimate in a 1-Wasserstein distance for the latter model showing that beam spreading is well captured by the Fermi pencil-beam approxi...
Preprint
Full-text available
In this work, we study a Lipschitz stability result in the reconstruction of a compactly supported initial temperature for the heat equation in $\mathbb{R}^n$, from measurements along a positive time interval and over an open set containing its support. We take advantage of the explicit dependency of solutions to the heat equation with respect to t...
Preprint
Full-text available
We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations by fractional Fermi pencil-beam models. We obtain an error estimate in a 1-Wasserstein distance for the latter model showing that beam spreading is well captured by the Fermi pencil-beam approxi...
Article
Full-text available
In X-ray CT scan with metallic objects, it is known that direct application of the filtered back-projection (FBP) formula leads to streaking artifacts in the reconstruction. These are characterized mathematically in terms of wave front sets in [13]. In this work, we give a quantitative microlocal analysis of such artifacts. We consider metal region...
Article
Full-text available
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time- convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters. Under the assumption of bei...
Article
Full-text available
It is well known that reconstruction algorithms in quantitative susceptibility mapping often contain streaking artifacts. These are nondesirable objects that contaminate the image, and the possibility of removing or at least reducing them has a great practical interest. In [J. K. Choi, H. S. Park, S. Wang, Y. Wang, and J. K. Seo, SIAM J. Imaging Sc...
Article
Full-text available
In this article we study the reconstruction problem in TAT/PAT on an attenuating media. Namely, we prove a reconstruction procedure of the initial condition for the damped wave equation via Neumann series that works for arbitrary large smooth attenuation coefficients extending the result of A. Homan. We also illustrate the theoretical result by inc...
Article
In this paper, we consider two linear plate models, namely the Reissner–Mindlin system (R–M) and the Kirchhoff–Love equation (K–L), which come from linear elasticity. We prove global Carleman inequalities for both models with boundary observations and under a suitable hypothesis on the parameters. We use these estimates to study the inverse problem...

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