16,671 research outputs found
On the Adjoint Operator in Photoacoustic Tomography
Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from
coupled physics" technique, in which the image contrast is due to optical
absorption, but the information is carried to the surface of the tissue as
ultrasound pulses. Many algorithms and formulae for PAT image reconstruction
have been proposed for the case when a complete data set is available. In many
practical imaging scenarios, however, it is not possible to obtain the full
data, or the data may be sub-sampled for faster data acquisition. In such
cases, image reconstruction algorithms that can incorporate prior knowledge to
ameliorate the loss of data are required. Hence, recently there has been an
increased interest in using variational image reconstruction. A crucial
ingredient for the application of these techniques is the adjoint of the PAT
forward operator, which is described in this article from physical, theoretical
and numerical perspectives. First, a simple mathematical derivation of the
adjoint of the PAT forward operator in the continuous framework is presented.
Then, an efficient numerical implementation of the adjoint using a k-space time
domain wave propagation model is described and illustrated in the context of
variational PAT image reconstruction, on both 2D and 3D examples including
inhomogeneous sound speed. The principal advantage of this analytical adjoint
over an algebraic adjoint (obtained by taking the direct adjoint of the
particular numerical forward scheme used) is that it can be implemented using
currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems
Identification of transient heat sources using the reciprocity gap
International audienceThe deformation of solid materials is nearly always accompanied with temperature variations, induced by intrinsic dissipation and thermomechanical coupling. Heat sources give precious information on the thermomechanical behavior of materials. They can be indirectly observed from thermal measurements on the specimen boundary, obtained e.g. via infrared thermography. To solve the inverse problem of identifying heat sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap Method is proposed. This approach, used elsewhere mainly for time-independent identification, is applied here to transient measurements. Under appropriate modelling assumptions the number of heat sources, their spatial locations and energies are retrieved, as demonstrated on numerical experiments where the robustness of the method to measurement noise is also studied
Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulation
Ultrasound-modulated optical tomography is an emerging biomedical imaging
modality which uses the spatially localised acoustically-driven modulation of
coherent light as a probe of the structure and optical properties of biological
tissues. In this work we begin by providing an overview of forward modelling
methods, before deriving a linearised diffusion-style model which calculates
the first-harmonic modulated flux measured on the boundary of a given domain.
We derive and examine the correlation measurement density functions of the
model which describe the sensitivity of the modality to perturbations in the
optical parameters of interest. Finally, we employ said functions in the
development of an adjoint-assisted gradient based image reconstruction method,
which ameliorates the computational burden and memory requirements of a
traditional Newton-based optimisation approach. We validate our work by
performing reconstructions of optical absorption and scattering in two- and
three-dimensions using simulated measurements with 1% proportional Gaussian
noise, and demonstrate the successful recovery of the parameters to within
+/-5% of their true values when the resolution of the ultrasound raster probing
the domain is sufficient to delineate perturbing inclusions.Comment: 12 pages, 6 figure
- …