TUM Library

Cover; Half Title; Title Page; Copyright Page; Contents; Preface; About the Editors; Contributors; I Introduction; 1 Materials Science vs. Data Science; II Emerging Data Science in Microstructure Characterization; 2 Emerging Digital Data Capabilities; 2.1 Introduction; 2.2 Benefits of Large Data Volumes; 2.3 Challenges of Large Data Volumes; 2.4 Emerging Techniques; 2.4.1 Multi-Instrument Coordination; 2.4.2 Upstream Data Analysis; 2.4.3 Data Mining; 2.4.4 Data Curation; 2.5 Conclusions; 3 Cultural Differences; 3.1 What Makes Modern Image Processing So Modern?

3.2 Language of Image Processing3.2.1 Notational Differences; 3.2.1.1 Sets; 3.2.1.2 Operations on Sets; 3.2.1.3 Computations on Sets; 3.2.2 Bayesian Probability and Image Processing; 3.2.2.1 Modern Probability and Sets; 3.2.2.2 Foundational Rules of Modern Probability; 3.2.2.3 Mathematical Constructs; 3.2.2.4 Bayesian Probability in Image Processing; 3.3 Language of Materials Science; 3.3.1 Thermodynamic Phases; 3.3.2 Free Energies; 3.4 Concluding Remarks; 4 Forward Modeling; 4.1 What Is Forward Modeling?; 4.1.1 What Are the Unknowns in Materials Characterization?

4.1.2 A Schematic Description of Forward Modeling4.2 A Brief Overview of Electron Scattering Modalities; 4.3 Case Studies; 4.3.1 Electron Backscatter Diffraction; 4.3.1.1 BSE Monte Carlo Simulations; 4.3.1.2 Dynamical Scattering Simulations; 4.3.1.3 Detector Parameters; 4.3.2 Lorentz Vector Field Electron Tomography; 4.3.2.1 Lorentz Forward Model; 4.3.2.2 Electron Wave Phase Shift Computations; 4.3.2.3 Example Lorentz Image Simulation; 4.4 Summary; 5 Inverse Problems and Sensing; 5.1 Introduction; 5.2 Traditional Approaches to Inversion; 5.3 Bayesian and Regularized Approaches to Inversion

5.4 Why Does Bayesian Estimation Work?5.5 Model-Based Reconstruction; 5.6 Successes and Opportunities of Bayesian Inversion; III Inverse Methods for Analysis of Data; 6 Model-Based Iterative Reconstruction for Electron Tomography; 6.1 Introduction; 6.2 Model-Based Iterative Reconstruction; 6.3 High-Angle Annular Dark-Field STEM Tomography; 6.3.1 HAADF-STEM Forward Model; 6.3.2 Prior Model; 6.3.3 Cost Function Formulation and Optimization Algorithm; 6.3.4 Experimental Results; 6.3.4.1 Simulated Dataset; 6.3.4.2 Experimental Dataset; 6.4 Bright-Field Electron Tomography

6.4.1 BF-TEM Forward Model and Cost Function Formulation6.4.1.1 Generalized Huber Functions for Anomaly Modeling; 6.4.1.2 MBIR Cost Formulation; 6.4.2 Results; 6.4.2.1 Simulated Dataset; 6.4.2.2 Real Dataset; 6.5 Future Directions; 6.6 Conclusion; 7 Statistical Reconstruction and Heterogeneity Characterization in 3-D Biological Macromolecular Complexes; 7.1 Introduction; 7.2 Statistical 3-D Signal Reconstruction of Macromolecular Complexes; 7.2.1 Introduction; 7.2.2 Statistical Model; 7.2.3 Relationship between the Moments of the Weights and the Moments of the Electron Scattering Intensity

Data analytics has become an integral part of materials science. This book provides the practical tools and fundamentals needed for researchers in materials science to understand how to analyze large datasets using statistical methods, especially inverse methods applied to microstructure characterization. It contains valuable guidance on essential topics such as denoising and data modeling. Additionally, the analysis and applications section addresses compressed sensing methods, stochastic models, extreme estimation, and approaches to pattern detection.

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