Inverse Problems and Applications.

Intro -- Preface -- Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by anomalous localized resonance II -- 1. Introduction -- 2. Layer potential formulation -- 3. Eigenvalues of the NP operator -- 4. Anomalous localized resonance in two dimensions -- 5. Non-occurrence of CALR in three dimensions -- References -- Hybrid inverse problems and redundant systems of partial differential equations -- 1. Introduction -- 2. Inverse Problems with local internal functionals. -- 3. Injectivity results for the linearized problem -- 4. Local uniqueness for nonlinear inverse problem -- Acknowledgment -- Appendix A. Unique continuation for redundant systems -- References -- A Direct Imaging Method for Inverse Scattering Using the Generalized Foldy-Lax Formulation -- 1. Introduction -- 2. Generalized Foldy-Lax formulation -- 3. Response matrix -- 4. Numerical experiments -- 5. Conclusion -- Appendix A. Orthogonal projection of response matrix -- References -- The Inverse Scattering Problem for a Penetrable Cavity with Internal Measurements -- 1. Introduction -- 2. The direct and inverse scattering problems -- 3. The exterior transmission eigenvalue problem -- 4. Uniqueness of the inverse problem -- 5. The solution of the inverse problem -- References -- A Neumann series based method for photoacoustic tomography on irregular domains -- 1. Introduction -- 2. Background -- 3. The reconstruction method -- 4. Numerical examples -- 5. Conclusion -- References -- Nonlinear Inversion from Partial EIT Data:Computational Experiments -- 1. Introduction -- 2. Method 1: The method based on the Schrödinger equation -- 3. Method 2: The method based on a ∂_{ } and \overline{∂}_{ } system -- 4. Computation of Partial Boundary Data CGO Solutions -- 5. Numerical Reconstruction of Conductivities from Partial Data Using Method 2.

6. Computational Experiments -- 7. Conclusions -- Acknowledgments -- References -- Increasing stability of the inverse boundary value problem for the Schrödinger equation -- 1. Introduction -- 2. Preliminaries -- 3. Proof of main theorem -- 4. Conclusion -- Acknowledgements -- References -- Recent progress of inverse scattering theory on non-compact manifolds -- 1. Introduction -- 2. Review of forward and inverse problems -- 3. Bird's-eye view of the inverse scattering problem for the metric -- 4. Examples -- 5. Arithmetic surface and generalized S-matrix -- 6. Works in progress -- References -- On an inverse problem for the Steklov spectrum of a Riemannian surface -- 1. Introduction -- 2. The problem of determining a metric on the disc -- 3. The problem of determining a positive function on the circle -- 4. The problem of recovering a planar domain -- 5. Two classes of Riemannian metrics -- 6. A scalar Riemann -Hilbert problem -- Appendix A. Proofs of Theorems 5.1 and 5.2 and of Lemma 6.2 -- References -- Recent progress in the Calderón problem with partial data -- 1. Introduction -- 2. Partial data results -- 3. Strategy of proof -- 4. Carleman estimates -- 5. Complex geometrical optics -- 6. Uniqueness results -- 7. The linearized case -- 8. Open problems -- References -- Local reconstruction of a Riemannian manifold from a restriction of the hyperbolic Dirichlet-to-Neumann operator -- 1. Introduction -- 2. The proof -- References -- Damping Mechanisms for Regularized Transformation-acoustics Cloaking -- 1. Introduction -- 2. The high-density scheme -- 3. The high-loss scheme -- References -- Hybrid Inverse Problem for Porous Media -- 1. Introduction -- 2. Model -- 3. Inverse Problem -- References -- Efficient Algorithms for Ptychographic Phase Retrieval -- 1. Introduction -- 2. Ptychographic reconstruction as an inverse problem.

3. Iterative algorithms based on nonlinear optimization -- 4. Numerical examples -- 5. Conclusion -- Acknowledgment -- References -- Matrix elements of Fourier Integral Operator -- 1. Background -- 2. Invariant states on ⁰( × , ): Proof of Propositions 1 and 2 -- 3. Almost orthogonality: Proof of Proposition 3 -- 4. Modulus squares as matrix elements -- 5. Proof of Proposition 4 -- 6. Isometries and Hecke operators -- References.

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