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.
- 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.
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.
