106 research outputs found
On the microlocal analysis of the geodesic X-ray transform with conjugate points
We study the microlocal properties of the geodesic X-ray transform
on a manifold with boundary allowing the presence of conjugate
points. Assuming that there are no self-intersecting geodesics and all
conjugate pairs are nonsingular we show that the normal operator can be decomposed as the sum of a
pseudodifferential operator of order and a sum of Fourier integral
operators. We also apply this decomposition to prove inversion of
is only mildly ill-posed in dimension three or higher
A Multi-Grid Iterative Method for Photoacoustic Tomography
Inspired by the recent advances on minimizing nonsmooth or bound-constrained
convex functions on models using varying degrees of fidelity, we propose a line
search multigrid (MG) method for full-wave iterative image reconstruction in
photoacoustic tomography (PAT) in heterogeneous media. To compute the search
direction at each iteration, we decide between the gradient at the target
level, or alternatively an approximate error correction at a coarser level,
relying on some predefined criteria. To incorporate absorption and dispersion,
we derive the analytical adjoint directly from the first-order acoustic wave
system. The effectiveness of the proposed method is tested on a total-variation
penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated
variant (FISTA), which have been used in many studies of image reconstruction
in PAT. The results show the great potential of the proposed method in
improving speed of iterative image reconstruction
The weighted doppler transform
We consider the tomography problem of recovering a covector field on a simple
Riemannian manifold based on its weighted Doppler transformation over a family
of curves . This is a generalization of the attenuated Doppler
transform. Uniqueness is proven for a generic set of weights and families of
curves under a condition on the weight function. This condition is satisfied in
particular if the weight function is never zero, and its derivatives along the
curves in is never zero
A continuous adjoint for photo-acoustic tomography of the brain
We present an optimization framework for photo-acoustic tomography of brain
based on a system of coupled equations that describe the propagation of sound
waves in linear isotropic inhomogeneous and lossy elastic media with the
absorption and physical dispersion following a frequency power law using
fractional Laplacian operators. The adjoint of the associated continuous
forward operator is derived, and a numerical framework for computing this
adjoint based on a k- space pseudospectral method is presented. We analytically
show that the derived continuous adjoint matches the adjoint of an associated
discretised operator. We include this adjoint in a first-order positivity
constrained optimization algorithm that is regularized by total variation
minimization, and show that the iterates monotonically converge to a minimizer
of an objective function, even in the presence of some error in estimating the
physical parameters of the medium.Comment: 28 pages, 24 figure (eps
- β¦