Preface ........................................................ ix
Hongkai Zhao
Introduction .................................................... 1
Bin Dong and Zuowei Shen
MRA-Based Wavelet Frames and Applications ....................... 7
Introduction .................................................... 9
Lecture 1 Multiresolution analysis ............................ 13
1 Definitions and basics ...................................... 13
2 Density of the union of Vn .................................. 15
3 Triviality of the intersections of Vn ....................... 17
4 Approximation ............................................... 20
Lecture 2 MRA-based tight wavelet frames ...................... 27
1 Extension principles ........................................ 29
2 Quasi-affine systems and associated algorithms .............. 48
3 Higher dimension tight frame systems ........................ 58
Lecture 3 Pseudo-splines and tight frames ..................... 63
1 Definitions and basics ...................................... 63
2 Wavelets from pseudo-splines ................................ 73
3 Regularity of pseudo-splines ................................ 81
4 Two lemmata ................................................. 93
Lecture 4 Frame based image restorations ...................... 99
1 Modeling ................................................... 100
2 Balanced approach .......................................... 105
3 Analysis based approach .................................... 125
Lecture 5 Other applications of frames ....................... 133
1 Background and models ...................................... 133
2 Frame based blind deconvolution ............................ 139
3 Frame based image segmentation ............................. 142
4 Scene reconstruction from range data ....................... 145
Bibliography .................................................. 151
Michael Elad
Five Lectures on Sparse and Redundant Representations
Modelling of Images ........................................... 159
Preface ....................................................... 161
Lecture 1 Introduction to sparse approximations -
algorithms .................................................... 165
1 Motivation and the sparse-coding problem ................... 165
2 Greedy algorithms .......................................... 166
3 Relaxation algorithms ...................................... 167
4 A closer look at the unitary case .......................... 168
Lecture 2 Introduction to sparse approximations - theory ..... 171
1 Dictionary properties ...................................... 171
2 Theoretical guarantees - uniqueness for P0 ................. 174
3 Equivalence of the MP and BP for the exact case ............ 175
4 Theoretical guarantees - stability for (P0ϵ) ................ 179
5 Near-oracle performance in the noisy case .................. 180
Lecture 3 Sparse and redundant representation modelling ...... 181
1 Modelling data with sparse and redundant representations ... 181
2 The Sparseland prior ....................................... 182
3 Processing Sparseland signals .............................. 183
Lecture 4 First steps in image processing .................... 187
1 Image deblurring via iterative-shrinkage algorithms ........ 187
2 Image denoising ............................................ 189
3 Image inpainting ........................................... 192
4 Dictionary learning ........................................ 193
Lecture 5 Image processing - more practice ................... 195
1 Image denoising with a learned dictionary .................. 195
2 Image inpainting with dictionary learning .................. 197
3 Image scale-up with a pair of dictionaries ................. 197
4 Image compression using sparse representation .............. 200
5 Summary .................................................... 202
Bibliography ............................................... 205
J.M. Teran, J.L. Hellrung, Jr. and J. Hegemann
Simulation of Elasticity, Biomechanics, and Virtual Surgery ... 209
Introduction .................................................. 211
Real-time computing ........................................... 212
Lecture 1 Introduction to continuum mechanics and
elasticity .................................................... 213
1 Kinematics ................................................. 213
2 Basic balance laws ......................................... 214
3 Elasticity and constitutive modeling ....................... 214
4 Equilibrium and weak form .................................. 216
5 ID Elasticity .............................................. 217
6 Inversion .................................................. 218
7 Time stepping .............................................. 220
Lecture 2 Numerical solutions of the equations of
elasticity .................................................... 221
1 Numerical solution of Poisson's equation via the finite
element method ............................................. 221
2 Neo-Hookean elasticity with quasistatic evolution in
dimension 1 ................................................ 224
3 Neo-Hookean elasticity with backward Euler evolution in
dimension 2 ................................................ 230
Lecture 3 Supplemental material .............................. 239
1 Handling inversion via diagonalization ..................... 239
2 Constitutive model for muscle .............................. 240
3 Guaranteeing positive definiteness of the linear systems
in Newton iterations ....................................... 241
Bibliography .................................................. 245
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