Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply...

Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

The standard approach to the solution of the adjoint equations stresses the similarity of direct and adjoint equations and implies the use of similar methods for their solution. Nevertheless, the adjoint equations have significant peculiarities in comparison with the direct problem equations at least for compressible flows. From a numerical viewpoint these features concern the existence of the ...

In this work we consider the problem on group classification and conservation laws of general first order evolution equations. We obtain subclasses these equations which are quasi-self-adjoint self-adjoint. By using recent Ibragimov's Theorem laws, establish admiting self-adjoint illustrate our results applying them to inviscid Burgers' equation. particular an infinite number new symmetries fou...

We consider the numerical solution of an inverse problem of finding the shape and location of holes in an elastic body. The problem is solved by minimizing a functional depending on the eigenvalues and traces of corresponding eigenmodes. We use the adjoint method to calculate the shape derivative of this functional. The optimization is performed by BFGS, using a genetic algorithm as a preproces...

We propose elastic isotropic wavefield tomography formulated with the misfit of observed and recorded data as the objective function. The adjoint-state method enables efficient calculation of the gradient of this data misfit function. We solve this optimization problem with the gradient-descent method in order to update the model parameters iteratively. Using the elastic isotropic wave-equation...