- Page 1 and 2: SPARSE IMAGE REPRESENTATION VIA COM
- Page 3: I certify that I have read this dis
- Page 7: To find a sparse image representati
- Page 12 and 13: xii
- Page 14 and 15: 2.3 Discussion.....................
- Page 16 and 17: 6 Simulations 119 6.1 Dictionary...
- Page 18 and 19: xviii
- Page 21 and 22: List of Figures 2.1 Shannon’s sch
- Page 23 and 24: A.3 Edgelet transform of the wood g
- Page 25 and 26: Nomenclature Special sets N .......
- Page 27 and 28: List of Abbreviations BCR .........
- Page 29 and 30: Chapter 1 Introduction 1.1 Overview
- Page 31 and 32: Chapter 2 Sparsity in Image Coding
- Page 33 and 34: 2.1. IMAGE CODING 5 INFORMATION SOU
- Page 35 and 36: 2.1. IMAGE CODING 7 2.1.2 Source an
- Page 37 and 38: 2.1. IMAGE CODING 9 x ✲ T y ERROR
- Page 39 and 40: 2.1. IMAGE CODING 11 where Q stands
- Page 41 and 42: 2.2. SPARSITY AND COMPRESSION 13 Pr
- Page 43 and 44: 2.2. SPARSITY AND COMPRESSION 15 av
- Page 45 and 46: 2.2. SPARSITY AND COMPRESSION 17 wi
- Page 47 and 48: 2.2. SPARSITY AND COMPRESSION 19 lo
- Page 49 and 50: 2.3. DISCUSSION 21 tail compact. Th
- Page 51 and 52: 2.4. PROOF 23 The index l does not
- Page 53 and 54: Chapter 3 Image Transforms and Imag
- Page 55 and 56: 27 Some of the figures show the bas
- Page 57 and 58: 3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 59 and 60:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 61 and 62:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 63 and 64:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 65 and 66:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 67 and 68:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 69 and 70:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 71 and 72:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 73 and 74:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 75 and 76:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 77 and 78:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 79 and 80:
3.1. DCT AND HOMOGENEOUS COMPONENTS
- Page 81 and 82:
3.2. WAVELETS AND POINT SINGULARITI
- Page 83 and 84:
3.2. WAVELETS AND POINT SINGULARITI
- Page 85 and 86:
3.2. WAVELETS AND POINT SINGULARITI
- Page 87 and 88:
3.2. WAVELETS AND POINT SINGULARITI
- Page 89 and 90:
3.2. WAVELETS AND POINT SINGULARITI
- Page 91 and 92:
3.2. WAVELETS AND POINT SINGULARITI
- Page 93 and 94:
3.3. EDGELETS AND LINEAR SINGULARIT
- Page 95 and 96:
3.4. OTHER TRANSFORMS 67 uncertaint
- Page 97 and 98:
3.4. OTHER TRANSFORMS 69 Chirplets
- Page 99 and 100:
3.4. OTHER TRANSFORMS 71 Folding. A
- Page 101 and 102:
3.4. OTHER TRANSFORMS 73 We can app
- Page 103 and 104:
3.5. DISCUSSION 75 give only a few
- Page 105 and 106:
3.7. PROOFS 77 the ijth component o
- Page 107 and 108:
3.7. PROOFS 79 Similarly, we have [
- Page 109 and 110:
Chapter 4 Combined Image Representa
- Page 111 and 112:
4.2. SPARSE DECOMPOSITION 83 interi
- Page 113 and 114:
4.3. MINIMUM l 1 NORM SOLUTION 85 l
- Page 115 and 116:
4.4. LAGRANGE MULTIPLIERS 87 ρ( x
- Page 117 and 118:
4.5. HOW TO CHOOSE ρ AND λ 89 3 (
- Page 119 and 120:
4.6. HOMOTOPY 91 A way to interpret
- Page 121 and 122:
4.7. NEWTON DIRECTION 93 4.7 Newton
- Page 123 and 124:
4.9. ITERATIVE METHODS 95 1. Avoidi
- Page 125 and 126:
4.11. DISCUSSION 97 ρ(β) =‖β
- Page 127 and 128:
4.12. PROOFS 99 4.12.2 Proof of The
- Page 129 and 130:
4.12. PROOFS 101 case of (4.16). Co
- Page 131 and 132:
Chapter 5 Iterative Methods This ch
- Page 133 and 134:
5.1. OVERVIEW 105 the k-th iteratio
- Page 135 and 136:
5.1. OVERVIEW 107 5.1.4 Preconditio
- Page 137 and 138:
5.2. LSQR 109 among all the block d
- Page 139 and 140:
5.2. LSQR 111 5.2.3 Algorithm LSQR
- Page 141 and 142:
5.3. MINRES 113 2. For k =1, 2,...,
- Page 143 and 144:
5.3. MINRES 115 using the precondit
- Page 145 and 146:
5.4. DISCUSSION 117 From (I + S 1 )
- Page 147 and 148:
Chapter 6 Simulations Section 6.1 d
- Page 149 and 150:
6.3. DECOMPOSITION 121 10 5 5 5 20
- Page 151 and 152:
6.4. DECAY OF COEFFICIENTS 123 10 2
- Page 153 and 154:
6.5. COMPARISON WITH MATCHING PURSU
- Page 155 and 156:
6.6. SUMMARY OF COMPUTATIONAL EXPER
- Page 157 and 158:
Chapter 7 Future Work In the future
- Page 159 and 160:
7.2. MODIFYING EDGELET DICTIONARY 1
- Page 161 and 162:
7.3. ACCELERATING THE ITERATIVE ALG
- Page 163 and 164:
Appendix A Direct Edgelet Transform
- Page 165 and 166:
A.2. EXAMPLES 137 edgelet transform
- Page 167 and 168:
A.3. DETAILS 139 (a) Stick image (b
- Page 169 and 170:
A.3. DETAILS 141 (a) Lenna image (b
- Page 171 and 172:
A.3. DETAILS 143 Ordering of Dyadic
- Page 173 and 174:
A.3. DETAILS 145 (1,K +1), (1,K +2)
- Page 175 and 176:
A.3. DETAILS 147 x 1 , y 1 x 2 , y
- Page 177 and 178:
Appendix B Fast Edgelet-like Transf
- Page 179 and 180:
B.1. TRANSFORMS FOR 2-D CONTINUOUS
- Page 181 and 182:
B.2. DISCRETE ALGORITHM 153 B.2.1 S
- Page 183 and 184:
B.2. DISCRETE ALGORITHM 155 extensi
- Page 185 and 186:
B.2. DISCRETE ALGORITHM 157 For the
- Page 187 and 188:
B.3. ADJOINT OF THE FAST TRANSFORM
- Page 189 and 190:
B.4. ANALYSIS 161 above matrix, whi
- Page 191 and 192:
B.5. EXAMPLES 163 B.5 Examples B.5.
- Page 193 and 194:
B.5. EXAMPLES 165 And so on. Note f
- Page 195 and 196:
B.6. MISCELLANEOUS 167 It takes abo
- Page 197 and 198:
B.6. MISCELLANEOUS 169 The function
- Page 199 and 200:
Bibliography [1] Sensor Data Manage
- Page 201 and 202:
BIBLIOGRAPHY 173 [24] C. Victor Che
- Page 203 and 204:
BIBLIOGRAPHY 175 [50] David L. Dono
- Page 205 and 206:
BIBLIOGRAPHY 177 [75] Vivek K. Goya
- Page 207 and 208:
BIBLIOGRAPHY 179 [100] Stéphane Ma
- Page 209 and 210:
BIBLIOGRAPHY 181 [127] C. E. Shanno