Browsing by Author "Palacios, Benjamin"

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    Fermi pencil beams and off-axis laser detection
    (2023) Bal, Guillaume; Palacios, Benjamin
    This paper concerns the analytic reconstruction of properties for narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements based on wide-angle single scattering of light detected away from the main path of the beam. Light propagation in the beam itself is modeled by macroscopic approximations of radiative transfer equations that take the form of Fermi pencil beam or fractional Fermi pencil beam equations. This allows for a simplified reconstruction procedure of the beam's constitutive parameters, in particular, its direction of propagation and the location of the emitting source. & COPY; 2023 Optica Publishing Group
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    PHOTOACOUSTIC TOMOGRAPHY IN ATTENUATING MEDIA WITH PARTIAL DATA
    (2022) Palacios, Benjamin
    The attenuation of ultrasound waves in photoacoustic and ther-moacoustic 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 inverse problem of initial source recovery with partial observations under the assumption of unique determination of the initial pressure. The main goal of this work is to fill this gap, this is, we prove the uniqueness property for the inverse prob-lem and establish the associated stability estimates as well. The problem of reconstructing the initial condition of acoustic waves in the complete-data set-ting is revisited and a new Neumann series reconstruction formula is obtained for the case of partial observations in a semi-bounded geometry. A numerical simulation is also included to test the method.
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    PSEUDODIFFERENTIAL MODELS FOR ULTRASOUND WAVES WITH FRACTIONAL ATTENUATION
    (2024) Acosta, Sebastian; Chan, Jesse; Johnson, Raven; Palacios, Benjamin
    To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Pade'\ approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Pade\' approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.