Mathematical and numerical approaches for multi-wave inverse problems : CIRM, Marseille, France, April 1-5, 2019 /: CIRM, Marseille, France, April 1-5, 2019. (2020)

• Record Type: Book
• Further Information: Note: Larisa Beilina, Maïtine Bergounioux, Michel Cristofol, Anabela Da Silva, Amelie Litman, editors.
• Other Names: Beilina, Larisa; Bergounioux, Maïtine; Cristofol, Michel; Da Silva, Anabela; Litman, Amelie; Centre national de rencontres mathématiques (France); Conference "Mathematical and Numerical Approaches for Multi-Wave Inverse Problems"
• Contents: Intro -- Preface -- Contents -- Thermoacoustic Applications -- 1 Introduction and Overview -- 2 Different Signal Generation Techniques -- 2.1 Propagating Electric Fields Induce Thermoacoustic Pulses -- 2.2 Photon Migration/Diffusion -- 2.3 Thermoacoustic Signals Generated by Charged Particles -- 3 Experimental Observations that Impact Data Analysis/Reconstruction -- 3.1 Co-locating Ultrasound Pulse-Echo and Thermoacoustic Receive Elements -- 3.2 Time Reversal -- References -- On the Transport Method for Hybrid Inverse Problems -- 1 Introduction -- 2 Proof of Theorem 1 -- References Stable Determination of an Inclusion in a Layered Medium with Special Anisotropy -- 1 Introduction -- 2 Notations and Main Result -- 3 Proof of the Main Result -- 4 Proof of Propositions 1 and 2 -- References -- Convergence of Stabilized P1 Finite Element Scheme for Time Harmonic Maxwell's Equations -- 1 Introduction -- 2 The Mathematical Model -- 3 Finite Element Method -- 3.1 Stabilized Model -- 3.2 Finite Element Discretization -- 3.3 Error Analysis -- 4 Numerical Examples -- 5 Conclusion -- References -- Regularized Linear Inversion with Randomized Singular Value Decomposition 1 Introduction -- 2 Preliminaries -- 2.1 SVD and Pseudoinverse -- 2.2 Randomized SVD -- 3 Efficient Regularized Linear Inversion with RSVD -- 3.1 Truncated RSVD -- 3.2 Tikhonov Regularization -- 3.3 General Tikhonov Regularization -- 3.4 Dual Interpretation -- 4 Error Analysis -- 4.1 Truncated RSVD -- 4.2 Tikhonov Regularization -- 4.3 General Tikhonov Regularization -- 5 Numerical Experiments and Discussions -- 5.1 One-Dimensional Benchmark Inverse Problems -- 5.2 Convergence of the Algorithm -- 5.3 Electrical Impedance Tomography -- 6 Conclusion -- References Parameter Selection in Dynamic Contrast-Enhanced Magnetic Resonance Tomography -- 1 Introduction -- 2 Image Reconstruction in Radial DCE-MRI -- 2.1 Forward Problem -- 2.2 Inverse Problem of Dynamic Image Reconstruction -- 2.3 Regularization Parameter Selection -- 2.4 Temporal Regularization Parameter Selection -- 3 Materials and Methods -- 4 Results -- 5 Conclusions -- References -- Convergence of Explicit P1 Finite-Element Solutions to Maxwell's Equations -- 1 Introduction -- 2 The Model Problem -- 3 The Numerical Model -- 3.1 Space Semi-discretization -- 3.2 Full Discretization 3.3 Convergence Results -- 4 Numerical Validation -- 5 Conclusions -- References -- Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography -- 1 Introduction -- 2 Modelling the Optical Coherence Tomography Measurement -- 3 Domain Decomposition of the Solution -- 4 Wave Propagation Through a Scattering Layer -- 5 Recovering the Susceptibility with Optical Coherence Elastography -- References -- The Finite Element Method and Balancing Principle for Magnetic Resonance Imaging -- 1 Introduction -- 2 Statement of the Forward and Inverse MRI Problem
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (147 p.)
• Subjects: 515/.357; Inverse problems (Differential equations) -- Congresses; Mathematical modelling; Numerical analysis; Differential calculus & equations; Functional analysis & transforms; Mathematics -- Applied; Mathematics -- Number Systems; Mathematics -- Mathematical Analysis; Inverse problems (Differential equations); Electronic books; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783030486341; 3030486346
• Related ISBNs: 9783030486334
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.