17,849 research outputs found
Quantitative photoacoustic imaging in radiative transport regime
The objective of quantitative photoacoustic tomography (QPAT) is to
reconstruct optical and thermodynamic properties of heterogeneous media from
data of absorbed energy distribution inside the media. There have been
extensive theoretical and computational studies on the inverse problem in QPAT,
however, mostly in the diffusive regime. We present in this work some numerical
reconstruction algorithms for multi-source QPAT in the radiative transport
regime with energy data collected at either single or multiple wavelengths. We
show that when the medium to be probed is non-scattering, explicit
reconstruction schemes can be derived to reconstruct the absorption and the
Gruneisen coefficients. When data at multiple wavelengths are utilized, we can
reconstruct simultaneously the absorption, scattering and Gruneisen
coefficients. We show by numerical simulations that the reconstructions are
stable.Comment: 40 pages, 13 figure
Photo-acoustic tomography in a rotating setting
Photo-acoustic tomography is a coupled-physics (hybrid) medical imaging
modality that aims to reconstruct optical parameters in biological tissues from
ultrasound measurements. As propagating light gets partially absorbed, the
resulting thermal expansion generates minute ultrasonic signals (the
photo-acoustic effect) that are measured at the boundary of a domain of
interest. Standard inversion procedures first reconstruct the source of
radiation by an inverse ultrasound (boundary) problem and second describe the
optical parameters from internal information obtained in the first step.
This paper considers the rotating experimental setting. Light emission and
ultrasound measurements are fixed on a rotating gantry, resulting in a
rotation-dependent source of ultrasound. The two-step procedure we just
mentioned does not apply. Instead, we propose an inversion that directly aims
to reconstruct the optical parameters quantitatively. The mapping from the
unknown (absorption and diffusion) coefficients to the ultrasound measurement
via the unknown ultrasound source is modeled as a composition of a
pseudo-differential operator and a Fourier integral operator. We show that for
appropriate choices of optical illuminations, the above composition is an
elliptic Fourier integral operator. Under the assumption that the coefficients
are unknown on a sufficiently small domain, we derive from this a (global)
injectivity result (measurements uniquely characterize our coefficients)
combined with an optimal stability estimate. The latter is the same as that
obtained in the standard (non-rotating experimental) setting
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