Note: Intro -- Modeling Nanoscale Imagingin Electron Microscopy -- Preface -- Contents -- Kantianism at the Nano-scale -- 1 Introduction -- 2 Nano-Images: Seeing the Invisible? -- 3 The Epistemic Significance of Observability -- 4 A Neo-Kantian Understanding of Science -- 5 Nano-Images -- References -- The Application of Scanning Transmission Electron Microscopy (STEM) to the Study of Nanoscale Systems -- 1 Introduction -- 2 Z-Contrast Imaging in STEM -- 2.1 Basic Concepts of Z-contrast Imaging -- 2.2 Aberration Correction -- 2.3 Low-dose Imaging -- 3 Application to Nanoscale Systems -- 3.1 The Structure of Clathrates -- 3.2 Nitrogen Doping in GaAs -- 3.3 Structure/Composition Fluctuations at Dislocations in SrTiO3 -- 3.4 Size Distribution in Catalytic Nanoparticles -- 4 Conclusions -- References -- High Resolution Exit Wave Restoration -- 1 Introduction -- 2 The Wave Aberration Function -- 3 Partial Coherence -- 3.1 Coherence Envelopes -- 3.2 Beyond Envelope Functions -- 4 Linear and Non-Linear Imaging -- 5 Specimen Approximations -- 5.1 The Phase Object Approximation -- 5.2 The Phase Contrast Transfer Function -- 6 Aberration Measurement -- 6.1 Minimum Variance -- 6.2 Tilt-Induced Aberration Measurement -- 6.2.1 Tilt-Induced Image Displacements -- 6.2.2 Tilt-Induced Defocus and Astigmatism -- 6.2.3 Automated Diffractogram Fitting -- 6.3 Aberration Determination from Crystalline Materials -- 7 Restoration Filters -- 7.1 The Paraboloid Method -- 7.2 Improved Linear Restoration Filters -- 7.3 The Maximum Likelihood Method -- 7.4 Transport of Intensities -- 7.5 Exit Wave Restoration Using Aberration Corrected Images -- 7.6 Alternative Experimental Data Sets -- 8 Conclusions -- References -- Compressed Sensing and Electron Microscopy -- 1 Introduction -- 2 The Foundations of Compressed Sensing -- 2.1 Models Classes for Images -- 2.2 Sampling. , 2.3 Decoding in Compressed Sensing -- 2.4 Dealing with Noise -- 2.5 Summary -- 3 What Could Compressed Sensing Buy for Electron Microscopy? -- 3.1 High-Resolution 2D Images: Model Class 1 -- 3.1.1 Image Model and Data Acquisition -- 3.1.2 Sparsity for Model Class 1 -- 3.1.3 Measurements for Model Class 1 -- 3.1.4 Inversion and Sparse Recovery Techniques -- 3.2 Electron Tomography -- 3.2.1 Example 1 -- 3.2.2 Example 2 -- 3.2.3 Logan-Shepp-Type Phantom -- 4 Conclusions -- References -- High-Quality Image Formation by Nonlocal Means Applied to High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM) -- 1 Introduction -- 2 STEM Imaging -- 3 Formation of High-Quality Images from Low-Resolution/Noisy Images -- 4 Nonlocal Means Algorithms for Sequences of Micrographs -- 4.1 Nonlocal Means for Time Series -- 4.2 A Multistage Algorithm -- 4.2.1 The First Stage: Single Frame Denoising -- 4.2.2 The Second Stage: Registration of Denoised Frames -- 4.2.3 The Third Stage: Multiframe Image Formation-Averaging -- 4.3 M1 Catalyst Micrograph Formation -- 5 Zeolite Micrograph Formation -- 6 Conclusion -- References -- Center of Mass Operators for Cryo-EM-Theory and Implementation -- 1 Introduction -- 2 Problem Setup -- 3 The GCAR Algorithm -- 3.1 Problem's Discretization -- 3.2 Orientations Revealing Operator -- 3.3 Orientation Encoding Eigenvectors -- 3.4 Coordinates Unmixing -- 3.5 Examples -- 4 Orientations Refinement -- 5 Center Estimation -- 5.1 Shift Equations -- 5.2 Detecting Common Lines -- 5.3 Measuring the Shift Estimation Error -- 5.4 Examples -- 6 Reconstruction from Real Data -- 7 Summary and Outlook -- References -- Index.

Note: Cover -- Multiscale Wavelet Methods for Partial Differential Equations -- Copyright -- Contents -- Preface -- Contributors -- I. FEM-Like Multilevel Preconditioning -- Multilevel Solvers for Elliptic Problems on Domains -- 1 Introduction -- 2 Stable subspace splittings and iterative methods -- 3 Subspaces for bounded domains -- 4 Multilevel preconditioners of BPX type -- 5 Extensions -- References -- Wavelet-Like Methods in the Design of Efficient Multilevel Preconditioners for Elliptic PDEs -- 1 Introduction -- 2 Preliminaries and basic problems -- 3 Matrix conditioning and stable Riesz bases -- 4 Model problems -- 5 Multilevel direct decompositions -- 6 The hierarchical basis -- 7 A stable Rieze basis by wavelet method -- 8 Implementations for a model problem -- 9 Numerical experiments -- References -- II. Fast Wavelet Algorithms: Compression and Adaptivity -- An Adaptive Collocation Method based on Interpolating Wavelets -- 1 Intorduction -- 2 Deslaurier-Dubuc interpolating wavelets -- 3 Wavelet collocation on uniform grids -- 4 Collocation on nonuniform grids -- 5 The adaptive scheme -- 6 Numerical tests -- 7 Conclusions -- References -- An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial Differential Equations -- 1 Introduction -- 2 The semigroup approach and quadratures -- 3 Preliminaries and conventions of wavelet analysis -- 4 Nonstandard form representation of operator functions -- 5 Evaluating functions in wavelet bases -- 6 Results of numerical experiments -- 7 Conclusions -- References -- A Dynamical Adaptive Concept Based on Wavelet Packet Best Bases: Application to Convection Diffusion Partial Differential Equations -- 1 Introduction -- 2 Basic aspects of wavelet packets -- 3 Numerical aspects of the wavelet packets -- 4 Topology of a wavelet packet in position-frequency space. , 5 Definition of the numerical scheme -- 6 Numerical results -- 7 Conclusion -- References -- Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations -- 1 Introduction -- 2 A class of elliptic problems -- 3 Smoothness spaces and wavelet decomposition -- 4 Linear approximation -- 5 Nonlinear wavelet approximation in L2(Ώ) -- 6 Regularity of solutions to PDE's and approximation order -- 7 An adaptive scheme for elliptic equations -- References -- III. Wavelet Solvers for Integral Equations -- Fully Discrete Multiscale Galerkin BEM -- 1 Introduction -- 2 Strongly elliptic boundary integral equations -- 3 Multiscale Galerkin boundary elements -- 4 Quadrature error analysis -- 5 Conclusion -- 6 Appendix -- References -- Wavelet Multilevel Solvers for Linear Ill-Posed Problems Stabilized by Tikhonov Regularization -- 1 Introduction -- 2 Preliminary considerations -- 3 The additive and multiplicative Schwarz methods -- 4 Application to integral equations -- References -- IV. Software Tools and Numerical Experiments -- Towards Object Oriented Software Tools for Numerical Multiscale Methods for PDEs using Wavelets -- 1 Introduction -- 2 Basic linear algebra tools -- 3 Multiscale methods -- 4 Outlook -- 5 Examples -- References -- Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems -- 1 Introduction -- 2 Multilevel framework -- 3 AFIF elements -- 4 Numerical examples -- References -- V. Multiscale Interaction and Applications to Turbulence -- Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation -- 1 Introduction -- 2 Near optimality of wavelets and symmetry breaking local models -- 3 Wavelet projections of the KS equation for short systems -- 4 O(2)-symmetric local models for the KS equation -- 5 Statistics of the large scales of the KS equation. , 6 Conclusion -- References -- Theoretical Dimension and the Complexity of Simulated Turbulence -- 1 Introduction -- 2 Techniques -- 3 Results -- 4 Discussion -- References -- VI: Wavelet Analysis of Partial Differential Operators -- Analysis of Second Order Elliptic Operators Without Boundary Conditions and With VMO or Hölderian Coefficients -- 1 Introduction -- 2 Preliminaries -- 3 The VMO case -- 4 The Hölderian case -- 5 The Galerkin approximation of the resolvent of L -- 6 Conclusion -- References -- Some Directional Elliptic Regularity For Domains With Cusps -- 1 Introduction -- 2 The basic formulas of continuous wavelet analysis -- 3 Some function spaces -- 4 More general microlocal classes -- 5 Some directional microlocal classes -- References -- Subject Index.

Note: Literaturverzeichnis: Seite 24-25

Note: Literaturverzeichnis: Seite 52-54

Note: Literaturverzeichnis: Seite 24-25

Note: Literaturverzeichnis: Seite 37-40

Note: Literaturverzeichnis: Seite 11

Note: Literaturverzeichnis: Seite 36

Note: Literaturverzeichnis: Seite 9-10