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
