Optical tomography: forward and inverse problems

Arridge, Simon; Schotland, John C.

doi:10.1088/0266-5611/25/12/123010

Cited by 620 publications

(678 citation statements)

References 200 publications

Supporting

Mentioning

661

Contrasting

Unclassified

Order By: Relevance

“…A taxonomy of algorithms is described by Arridge & Schotland [12], and some comparisons on a test case are presented by Schweiger & Arridge [13]. In the remainder, we focus only on the regularized output least-squares method.…”

Section: (E) Reconstruction Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Methods in diffuse optical imaging

Arridge

2011

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

Section: (E) Reconstruction Methodsmentioning

confidence: 99%

“…Another form of coupled second-order PDEs is obtained through the even-parity RTE, which generalizes the DA derivation to higher orders of the P N approximation. It takes the form 12) where f + (ŝ) = 1 2 (f(ŝ) + f(−ŝ)) and C and K are generalized absorption and diffusion operators, respectively [4].…”

Section: (I) the Radiative Transfer Equationmentioning

confidence: 99%

Methods in diffuse optical imaging

Arridge

2011

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…The next section will discuss dual consistency of the time quadratures for Runge-Kutta DG discretizations (assumed to be dual consistent in space). Consider again equation (1). For simplicity of exposition, we rewrite (1) in the form:…”

Section: Space-time Duality Relations In Function Spacesmentioning

confidence: 99%

“…IPs arise in various applications of engineering and mathematics, e.g., seismography, meteorology, oceanography, medical imaging, systems biology, and fluid dynamics (see, e.g., [1,2,3,4,5,6]). IPs are usually described as constrained optimization problems, where the constraints are ordinary (ODE) or partial differential equations (PDEs).…”

Section: Introductionmentioning

confidence: 99%

Space–time adaptive solution of inverse problems with the discrete adjoint method

Alexe

Sandu

2014

Journal of Computational Physics

View full text Add to dashboard Cite

Abstract. Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the intergrid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided for the discontinuous Galerkin (DG) method. The adjoint model development is considerably simplified by decoupling the adaptive mesh refinement mechanism from the forward model solver, and by selectively applying automatic differentiation on individual algorithms.In forward models discontinuous Galerkin discretizations can efficiently handle high orders of accuracy, h/p-refinement, and parallel computation. The analysis reveals that this approach, paired with Runge Kutta time stepping, is well suited for the adaptive solutions of inverse problems. The usefulness of discrete discontinuous Galerkin adjoints is illustrated on a two-dimensional adaptive data assimilation problem. Space-time adaptive solution of inverse problems with the discrete adjoint method2

show abstract

“…The radiative transport equation is used in various subfields in science and engineering 4 such as light propagation in biological tissue 1,3 , clouds, and ocean 45,47 , seismic waves 41 , light in the interstellar medium 10,40 , neutron transport 9 , and remote sensing 23 . In these cases, usually three dimensions are most important.…”

Section: Introductionmentioning

confidence: 99%