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Chapter 12. Shape Reconstruction of Inverse Medium Scattering for the Helmholtz Equation

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Computational Methods for Applied Inverse Problems
This chapter is in the book Computational Methods for Applied Inverse Problems

Chapters in this book

  1. Frontmatter i
  2. Preface v
  3. Editor’s Preface vii
  4. Contents xi
  5. Part I. Introduction
  6. Chapter 1. Inverse Problems of Mathematical Physics 3
  7. Part II. Recent Advances in Regularization Theory and Methods
  8. Chapter 2. Using Parallel Computing for Solving Multidimensional Ill-posed Problems 49
  9. Chapter 3. Regularization of Fredholm Integral Equations of the First Kind using Nyström Approximation 65
  10. Chapter 4. Regularization of Numerical Differentiation: Methods and Applications 83
  11. Chapter 5. Numerical Analytic Continuation and Regularization 121
  12. Chapter 6. An Optimal Perturbation Regularization Algorithm for Function Reconstruction and Its Applications 143
  13. Chapter 7. Filtering and Inverse Problems Solving 169
  14. Part III. Optimal Inverse Design and Optimization Methods
  15. Chapter 8. Inverse Design of Alloys’ Chemistry for Specified Thermo-Mechanical Properties by using Multi-objective Optimization 197
  16. Chapter 9. Two Approaches to Reduce the Parameter Identification Errors 221
  17. Chapter 10. A General Convergence Result for the BFGS Method 241
  18. Part IV. Recent Advances in Inverse Scattering
  19. Chapter 11. Uniqueness Results for Inverse Scattering Problems 251
  20. Chapter 12. Shape Reconstruction of Inverse Medium Scattering for the Helmholtz Equation 283
  21. Part V. Inverse Vibration, Data Processing and Imaging
  22. Chapter 13. Numerical Aspects of the Calculation of Molecular Force Fields from Experimental Data 309
  23. Chapter 14. Some Mathematical Problems in Biomedical Imaging 331
  24. Part VI Numerical Inversion in Geosciences
  25. Chapter 15. Numerical Methods for Solving Inverse Hyperbolic Problems 369
  26. Chapter 16. Inversion Studies in Seismic Oceanography 395
  27. Chapter 17. Image Resolution Beyond the Classical Limit 411
  28. Chapter 18. Seismic Migration and Inversion 439
  29. Chapter 19. Seismic Wavefields Interpolation Based on Sparse Regularization and Compressive Sensing 475
  30. Chapter 20. Some Researches on Quantitative Remote Sensing Inversion 509
  31. Index 529
https://doi.org/10.1515/9783110259056.283

Chapters in this book

  1. Frontmatter i
  2. Preface v
  3. Editor’s Preface vii
  4. Contents xi
  5. Part I. Introduction
  6. Chapter 1. Inverse Problems of Mathematical Physics 3
  7. Part II. Recent Advances in Regularization Theory and Methods
  8. Chapter 2. Using Parallel Computing for Solving Multidimensional Ill-posed Problems 49
  9. Chapter 3. Regularization of Fredholm Integral Equations of the First Kind using Nyström Approximation 65
  10. Chapter 4. Regularization of Numerical Differentiation: Methods and Applications 83
  11. Chapter 5. Numerical Analytic Continuation and Regularization 121
  12. Chapter 6. An Optimal Perturbation Regularization Algorithm for Function Reconstruction and Its Applications 143
  13. Chapter 7. Filtering and Inverse Problems Solving 169
  14. Part III. Optimal Inverse Design and Optimization Methods
  15. Chapter 8. Inverse Design of Alloys’ Chemistry for Specified Thermo-Mechanical Properties by using Multi-objective Optimization 197
  16. Chapter 9. Two Approaches to Reduce the Parameter Identification Errors 221
  17. Chapter 10. A General Convergence Result for the BFGS Method 241
  18. Part IV. Recent Advances in Inverse Scattering
  19. Chapter 11. Uniqueness Results for Inverse Scattering Problems 251
  20. Chapter 12. Shape Reconstruction of Inverse Medium Scattering for the Helmholtz Equation 283
  21. Part V. Inverse Vibration, Data Processing and Imaging
  22. Chapter 13. Numerical Aspects of the Calculation of Molecular Force Fields from Experimental Data 309
  23. Chapter 14. Some Mathematical Problems in Biomedical Imaging 331
  24. Part VI Numerical Inversion in Geosciences
  25. Chapter 15. Numerical Methods for Solving Inverse Hyperbolic Problems 369
  26. Chapter 16. Inversion Studies in Seismic Oceanography 395
  27. Chapter 17. Image Resolution Beyond the Classical Limit 411
  28. Chapter 18. Seismic Migration and Inversion 439
  29. Chapter 19. Seismic Wavefields Interpolation Based on Sparse Regularization and Compressive Sensing 475
  30. Chapter 20. Some Researches on Quantitative Remote Sensing Inversion 509
  31. Index 529
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