| Preface |
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ix | |
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| Introduction |
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1 | (6) |
| MRA-Based Wavelet Frames and Applications |
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7 | (2) |
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| Introduction |
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9 | (150) |
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Lecture 1 Multiresolution analysis |
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13 | (14) |
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13 | (2) |
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2 Density of the union of Vn |
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15 | (2) |
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3 Triviality of the intersections of Vn |
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17 | (3) |
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20 | (7) |
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Lecture 2 MRA-based tight wavelet frames |
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27 | (36) |
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29 | (19) |
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2 Quasi-affine systems and associated algorithms |
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48 | (10) |
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3 Higher dimension tight frame systems |
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58 | (5) |
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Lecture 3 Pseudo-splines and tight frames |
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63 | (36) |
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63 | (10) |
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2 Wavelets from pseudo-splines |
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73 | (8) |
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3 Regularity of pseudo-splines |
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81 | (12) |
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93 | (6) |
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Lecture 4 Frame based image restorations |
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99 | (34) |
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100 | (5) |
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105 | (20) |
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3 Analysis based approach |
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125 | (8) |
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Lecture 5 Other applications of frames |
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133 | (26) |
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133 | (6) |
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2 Frame based blind deconvolution |
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139 | (3) |
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3 Frame based image segmentation |
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142 | (3) |
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4 Scene reconstruction from range data |
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145 | (6) |
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151 | (8) |
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Five Lectures on Sparse and Redundant Representations Modelling of Images |
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159 | (50) |
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161 | (4) |
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Lecture 1 Introduction to sparse approximations - algorithms |
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165 | (6) |
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1 Motivation and the sparse-coding problem |
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165 | (1) |
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166 | (1) |
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167 | (1) |
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4 A closer look at the unitary case |
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168 | (3) |
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Lecture 2 Introduction to sparse approximations - theory |
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171 | (10) |
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171 | (3) |
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2 Theoretical guarantees - uniqueness for P0 |
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174 | (1) |
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3 Equivalence of the MP and BP for the exact case |
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175 | (4) |
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4 Theoretical guarantees - stability for (Pε0) |
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179 | (1) |
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5 Near-oracle performance in the noisy case |
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180 | (1) |
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Lecture 3 Sparse and redundant representation modelling |
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181 | (6) |
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1 Modelling data with sparse and redundant representations |
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181 | (1) |
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182 | (1) |
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3 Processing Sparseland signals |
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183 | (4) |
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Lecture 4 First steps in image processing |
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187 | (8) |
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1 Image deblurring via iterative-shrinkage algorithms |
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187 | (2) |
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189 | (3) |
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192 | (1) |
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193 | (2) |
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Lecture 5 Image processing - more practice |
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195 | (14) |
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1 Image denoising with a learned dictionary |
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195 | (2) |
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2 Image inpainting with dictionary learning |
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197 | (1) |
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3 Image scale-up with a pair of dictionaries |
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197 | (3) |
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4 Image compression using sparse representation |
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200 | (2) |
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202 | (3) |
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205 | (4) |
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Simulation of Elasticity, Biomechanics, and Virtual Surgery |
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209 | (36) |
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211 | (1) |
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212 | (1) |
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Lecture 1 Introduction to continuum mechanics and elasticity |
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213 | (8) |
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213 | (1) |
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214 | (1) |
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3 Elasticity and constitutive modeling |
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214 | (2) |
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4 Equilibrium and weak form |
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216 | (1) |
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217 | (1) |
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218 | (2) |
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220 | (1) |
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Lecture 2 Numerical solutions of the equations of elasticity |
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221 | (18) |
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1 Numerical solution of Poisson's equation via the finite element method |
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221 | (3) |
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2 Neo-Hookean elasticity with quasistatic evolution in dimension 1 |
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224 | (6) |
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3 Neo-Hookean elasticity with backward Euler evolution in dimension 2 |
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230 | (9) |
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Lecture 3 Supplemental material |
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239 | (6) |
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1 Handling inversion via diagonalization |
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239 | (1) |
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2 Constitutive model for muscle |
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240 | (1) |
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3 Guaranteeing positive definiteness of the linear systems in Newton iterations |
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241 | (4) |
| Bibliography |
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245 | |
