A fully non-linear optimization approach to acousto-electric tomography

DOI10.1088/1361-6420/aad6b1zbMath1397.78053arXiv1804.02507OpenAlexW3099806506WikidataQ60548983 ScholiaQ60548983MaRDI QIDQ4582725

Kim Knudsen, Souvik Roy, Bolaji James Adesokan, Venkateswaran P. Krishnan

Publication date: 24 August 2018

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02507

zbMATH Keywords

nonlinear conjugate gradienthybrid imagingnonlinear PDE optimizationacousto-electric tomography

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Biological applications of optics and electromagnetic theory (78A70) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Hydro- and aero-acoustics (76Q05) Existence theories for optimal control problems involving partial differential equations (49J20) Optimization problems in optics and electromagnetic theory (78M50)

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Cites Work

• Unnamed Item
• Cauchy problem for ultrasound-modulated EIT
• Inverse diffusion problems with redundant internal information
• A Fokker-Planck control framework for multidimensional stochastic processes
• On a counter-example to quantitative Jacobian bounds
• Stabilizing inverse problems by internal data. II: Non-local internal data and generic linearized uniqueness
• Overdetermined elliptic boundary-value problems
• Inverse diffusion from knowledge of power densities
• Critical points for elliptic equations with prescribed boundary conditions
• Mathematics of Photoacoustic and Thermoacoustic Tomography
• The Levenberg–Marquardt iteration for numerical inversion of the power density operator
• 2D and 3D reconstructions in acousto-electric tomography
• Stabilizing inverse problems by internal data
• Hybrid tomography for conductivity imaging
• Imaging by Modification: Numerical Reconstruction of Local Conductivities from Corresponding Power Density Measurements
• Hybrid inverse problems and redundant systems of partial differential equations
• Electrical Impedance Tomography by Elastic Deformation
• Impedance-Acoustic Tomography
• Uniqueness and convergence of conductivity image reconstruction in magnetic resonance electrical impedance tomography
• Propagation of singularities for linearised hybrid data impedance tomography
• Linear and Nonlinear Inverse Problems with Practical Applications
• A New Optimization Approach to Sparse Reconstruction of Log-Conductivity in Acousto-Electric Tomography
• On a Nonlinear Partial Differential Equation Arising in Magnetic Resonance Electrical Impedance Tomography
• Hybrid inverse problems and internal functionals
• A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
• Analysis of Finite Difference Schemes
• Stability of coupled-physics inverse problems with one internal measurement
• Univalent \(\sigma\)-harmonic mappings