Inverse Problems: Modelling and Simulation

This volume presents the latest theoretical and experimental advancements in the field of inverse problems in recent years. It includes outstanding research results that reflect current theoretical and numerical aspects of inverse problems and their various applications. The volume is a collection of selected contributions from nearly three hundred invited presentations at the International Conference "Inverse Problems: Modelling and Simulation" (IPMS 2024) held from May 26 to June 1, 2024, in Malta.

The topics covered in this volume are closely related to emerging deterministic and stochastic models in the fields of medical imaging, biology, geophysics, radar, computer science, communication theory, signal processing, visualization, engineering, and economics. The contributions in this volume reflect a broad range of problems in the theory and applications of inverse problems that are useful for mathematicians, physicists, engineers, and researchers working with inverse problems.

Provides an overview of the recent developments in the field of inverse problems Covers topics in medical imaging, biology, geophysics, computer science, signal processing, engineering and economics Fosters effective learning and collaboration

Autorentext

Alemdar Hasanov Hasanolu is a professor of mathematics at Kocaeli University in Türkiye.

Roman Novikov is a Directeur de recherche at CNRS-Centre National de la Recherche Scientifique at École polytechnique CMAP-Centre de Mathématiques Appliquées, France.

Karel Van Bockstal is a post-doctoral researcher (Ghent Analysis & PDE Center) at the Department of Mathematics: Analysis, Logic and Discrete Mathematics of Ghent University, Belgium.

Inhalt

• Part I: Detection Methods. - 1. Determination of cavities in nonlinear parabolic systems arising from electrophysiology.- 2. Source detection on a network: numerical considerations.- 3. Resonator-Based Mass Detection in Nanostructures.- 4. Exploring instabilities of inverse problem solvers with low-dimensional manifolds.- 5. The multifrequency topological derivative method as a data processing tool in nondestructive testing.- 6. Motion Detection in Diffraction Tomography.- Part II: Geometric Inverse Problems .- 7. Survey on Broken Ray Transforms.- 8. Inverse Problems for Twisted Geodesic Flows.- 9. Applications of momentum ray transforms in inverse problems.- Part III: Inverse and Control Problems in Vibrating Structures .- 10. On the use of a roving harmonic load to locate cracks in shear deformable beam.- 11. Identification of out-of-plane loads over Timoshenko beams.- 12. Inverse Source Problems of Damped Vibrating Beam and Plate Models.- Part IV: Inverse Problems and Imaging. - 13. Higher order autocorrelations.- 14. Inverse Problems in Image Restoration.- 15. A Counterexample to Convergence for Multiscale.- 16. Three-dimensional brassiere design for electrical impedance tomography and numerical conductivity reconstructions in EIDORS.- 17. Permittivity Estimation Using Plasmonics.- Part V: Inverse problems and Regularisation. - 18. On Fourier Phase Retrieval by Differential Intensity Measurements in Finite Dimensions.- 19. Bi-level regularization via iterative mesh refinement for aeroacoustics.- Part VI: Inverse Problems for Fractional Equations .- 20. The Inverse Problem for the Fractional Conductivity.- 21. Inverse problems for simultaneous determination of source terms and several scalar parameters of fractional diffusion equations.- 22. A local uniqueness theorem for the fractional Schr¨odinger equation on closed Riemannian manifolds.- 23. Time-fractional diffusion equations of piecewise constant time-varying order.- Part VII: Inverse Problems for PDEs .- 24. A global optimum-informed greedy algorithm for A-optimal experimental design.- 25. Multi-dimensional operators with Sonine kernels.- 26. Numerical Reconstruction of Orders in Coupled Systems of Subdiffusion Equations.- 27. Inverse problems for a wave equation with an interface.- 28. New derivation of relaxation tensor for anisotropic extended Burgers model.- 29. Inverse Problems for Screens.- 30. Shearlet localization operator and microlocal analysis.- 31. Strong Unique Continuation for the Damped Wave.- Part VIII: Inverse Scattering Problems .- 32. Reduced Order Lippmann-Schwinger-Lanczos Inverse Scattering Method.- 33. Transparent scatterers and transmission eigenvalues.- 34. On passive inverse obstacle scattering problems with Neumann and Robin boundary conditions.- 35. New series representations and reconstruction techniques in coefficient inverse problems.- 36. A method to extrapolate the data for the inverse magnetisation problem with a planar sample.- 37. Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrödinger equation in the resonance frequency domain.- Part IX: Machine Learning. - 38. Quantum-inspired classification algorithms.- Part X: Radon Transforms and Applications. - 39. Geometry of domains and algebraic type of their Radon transforms.- 40. Remarks on the Interior Problem for the Radon transform.- 41. Range conditions for some divergent-beam transforms.- 42. Super-resolution reconstruction from truncated Hankel transform.- Part XI: Stochastic Problems and Bayesian Inversion .- 43. Inverse stochastic variational formulation for a control economic equilibrium problem.- 44. Sampling in Bayesian inversion accelerated by surrogate models.