Preface |
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xi | |
Editors |
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xiii | |
Contributors |
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xv | |
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1 Image Denoising: Past, Present, and Future |
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1 | (24) |
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1 | (1) |
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1.2 Historical Review of Image Denoising |
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2 | (3) |
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1.3 First Episode: Local Wiener Filtering |
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5 | (3) |
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1.4 Second Episode: Understanding Transient Events |
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8 | (5) |
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1.4.1 Local Wiener Filtering in the Wavelet Space |
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8 | (1) |
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1.4.2 Wavelet vs. DCT Denoising |
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9 | (4) |
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1.5 Third Generation: Understanding Nonlocal Similarity |
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13 | (4) |
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1.6 Conclusions and Perspectives |
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17 | (8) |
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1.6.1 Representation versus Optimization |
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17 | (1) |
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1.6.2 Is Image Denoising Dead? |
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18 | (1) |
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18 | (7) |
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2 Fundamentals of Image Restoration |
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25 | (38) |
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25 | (1) |
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2.2 Linear Shift-Invariant Degradation Model |
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26 | (3) |
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2.3 Image Restoration Methods |
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29 | (17) |
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2.3.1 Least Squares Estimation |
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29 | (4) |
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2.3.2 Steepest Descent Approach |
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33 | (1) |
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2.3.3 Regularization Models |
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34 | (1) |
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35 | (1) |
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2.3.5 Regularization with lp Norm, O < p ≤ 1 |
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36 | (3) |
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39 | (1) |
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40 | (2) |
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2.3.8 Projection onto Convex Sets |
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42 | (2) |
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2.3.9 Learning-Based Image Restoration |
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44 | (2) |
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2.4 Blind Image Restoration |
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46 | (2) |
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2.4.1 Alternating Minimization |
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47 | (1) |
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2.4.2 Iterative Blind Deconvolution |
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48 | (1) |
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2.5 Other Methods of Image Restoration |
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48 | (2) |
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2.6 Super Resolution Image Restoration |
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50 | (1) |
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2.7 Regularization Parameter Estimation |
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51 | (1) |
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2.8 Beyond Linear Shift-Invariant Imaging Model |
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52 | (1) |
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53 | (10) |
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53 | (10) |
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3 Restoration in the Presence of Unknown Spatially Varying Blur |
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63 | (26) |
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63 | (1) |
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64 | (11) |
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70 | (2) |
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72 | (1) |
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3.2.3 Defocus and Aberrations |
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73 | (2) |
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3.3 Space-Variant Super Resolution |
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75 | (9) |
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75 | (2) |
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77 | (1) |
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78 | (2) |
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80 | (1) |
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3.3.5 Deconvolution and Super Resolution |
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80 | (3) |
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83 | (1) |
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84 | (5) |
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84 | (5) |
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4 Image Denoising and Restoration Based on Nonlocal Means |
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89 | (26) |
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89 | (3) |
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4.2 Image Denoising Based on the Nonlocal Means |
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92 | (7) |
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92 | (5) |
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4.2.2 Iterative NLM Denoising |
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97 | (2) |
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4.3 Image Deblurring Using Nonlocal Means Regularization |
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99 | (2) |
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4.3.1 Iterative Deblurring |
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99 | (1) |
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4.3.2 Iterative Deblurring with Nonlocal Means Regularization |
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100 | (1) |
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4.4 Recent Nonlocal and Sparse Modeling Methods |
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101 | (6) |
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4.5 Reducing Computational Cost of NLM-Based Methods |
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107 | (2) |
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109 | (6) |
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111 | (4) |
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5 Sparsity-Regularized Image Restoration: Locality and Convexity Revisited |
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115 | (26) |
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115 | (2) |
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5.2 Historical Review of Sparse Representations |
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117 | (1) |
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5.3 From Local to Nonlocal Sparse Representations |
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118 | (6) |
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5.3.1 Local Variations: Wavelets and Beyond |
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118 | (2) |
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5.3.2 Nonlocal Similarity: From Manifold Learning to Subspace Constraint Exploitation |
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120 | (4) |
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5.4 From Convex to Nonconvex Optimization Algorithms |
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124 | (3) |
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5.5 Reproducible Experimental Results |
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127 | (4) |
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127 | (1) |
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128 | (1) |
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129 | (2) |
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5.6 Conclusions and Connections |
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131 | (10) |
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133 | (8) |
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6 Resolution Enhancement Using Prior Information |
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141 | (34) |
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141 | (2) |
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6.2 Fourier Transform Estimation and Minimum L2-Norm Solution |
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143 | (3) |
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6.2.1 Hilbert Space Reconstruction Methods |
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143 | (1) |
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6.2.2 Minimum L2-Norm Solutions |
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144 | (1) |
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6.2.3 Case of Fourier-Transform Data |
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144 | (1) |
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6.2.4 Case of Under-Determined Systems of Linear Equations |
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145 | (1) |
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6.3 Minimum Weighted L2-Norm Solution |
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146 | (11) |
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6.3.1 Class of Inner Products |
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147 | (1) |
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6.3.2 Minimum T-Norm Solutions |
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148 | (1) |
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6.3.3 Case of Fourier-Transform Data |
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148 | (1) |
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6.3.4 Case of p(x) = Xx (x) |
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149 | (1) |
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150 | (3) |
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6.3.6 Multidimensional Problem |
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153 | (1) |
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6.3.7 Case of Radon-Transform Data: Tomographic Data |
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154 | (1) |
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6.3.8 Under-Determined Systems of Linear Equations |
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154 | (1) |
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155 | (2) |
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6.4 Solution Sparsity and Data Sampling |
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157 | (4) |
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157 | (1) |
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158 | (1) |
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158 | (2) |
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6.4.4 Tomographic Imaging |
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160 | (1) |
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6.4.5 Compressed Sampling |
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161 | (1) |
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6.5 Minimum L1-Norm and Minimum Weighted L1-Norm Solutions |
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161 | (3) |
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6.5.1 Minimum L1-Norm Solutions |
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161 | (1) |
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162 | (1) |
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6.5.3 Comparison with the PDFT |
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163 | (1) |
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6.5.4 Iterative Reweighting |
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163 | (1) |
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6.6 Modification with Nonuniform Weights |
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164 | (5) |
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6.6.1 Selection of Windows |
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164 | (1) |
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6.6.2 Multidimensional Case |
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165 | (1) |
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6.6.3 Challenge of the Modified PDFT for Realistic Applications |
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165 | (2) |
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6.6.4 Modified Strategy in the Choice of Weighted Windows |
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167 | (2) |
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6.7 Summary and Conclusions |
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169 | (6) |
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171 | (4) |
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7 Transform Domain-Based Learning for Super Resolution Restoration |
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175 | (42) |
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7.1 Introduction to Super Resolution |
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175 | (3) |
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7.1.1 Limitations of Imaging Systems |
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176 | (1) |
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7.1.2 Super Resolution Concept |
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176 | (1) |
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7.1.3 Super Resolution: Ill-Posed Inverse Problem |
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177 | (1) |
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178 | (5) |
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7.2.1 Motion-Based Super Resolution |
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178 | (2) |
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7.2.2 Motion-Free Super Resolution |
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180 | (1) |
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7.2.3 Learning-Based Super Resolution |
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181 | (2) |
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7.3 Description of the Proposed Approach |
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183 | (7) |
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7.3.1 Image Acquisition Model |
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184 | (1) |
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7.3.2 Learning the Initial HR Estimation |
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185 | (1) |
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7.3.3 Degradation Estimation |
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185 | (1) |
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7.3.4 Image Field Model and MAP Estimation |
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186 | (4) |
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7.3.5 Applying the Algorithm to Color Images |
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190 | (1) |
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7.4 Transform Domain-Based Learning of the Initial HR Estimate |
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190 | (10) |
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7.4.1 Learning the Initial HR Estimate Using DWT |
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191 | (2) |
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7.4.2 Initial Estimate Using Discrete Cosine Transform |
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193 | (4) |
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7.4.3 Learning the Initial HR Estimate Using Contourlet Transform |
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197 | (3) |
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200 | (7) |
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7.5.1 Construction of the Training Database |
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200 | (1) |
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7.5.2 Results on Gray-Scale Images |
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201 | (3) |
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7.5.3 Results on Color Images |
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204 | (3) |
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7.6 Conclusions and Future Research Work |
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207 | (10) |
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207 | (2) |
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7.6.2 Future Research Work |
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209 | (1) |
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210 | (7) |
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8 Super Resolution for Multispectral Image Classification |
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217 | (32) |
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217 | (3) |
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220 | (10) |
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220 | (2) |
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8.2.2 Super Resolution Based on a Universal Hidden Markov Tree Model |
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222 | (6) |
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8.2.3 MAP-uHMT on Multispectral Images |
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228 | (2) |
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230 | (15) |
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8.3.1 Testing with MODIS data |
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230 | (8) |
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8.3.2 Testing with ETM+ data |
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238 | (7) |
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245 | (4) |
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246 | (3) |
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9 Color Image Restoration Using Vector Filtering Operators |
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249 | (36) |
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249 | (1) |
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250 | (8) |
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9.2.1 Numeral Representation |
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251 | (1) |
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252 | (1) |
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253 | (3) |
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9.2.4 Distance and Similarity Measures |
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256 | (2) |
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9.3 Color Space Conversions |
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258 | (4) |
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9.3.1 Standardized Representations |
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258 | (1) |
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9.3.2 Luminance-Chrominance Representations |
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259 | (1) |
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9.3.3 Cylindrical Representations |
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260 | (2) |
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9.3.4 Perceptual Representations |
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262 | (1) |
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9.4 Color Image Filtering |
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262 | (12) |
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9.4.1 Order-Statistic Methods |
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263 | (7) |
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9.4.2 Combination Methods |
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270 | (4) |
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9.5 Color Image Quality Evaluation |
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274 | (3) |
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9.5.1 Subjective Assessment |
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274 | (1) |
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9.5.2 Objective Assessment |
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275 | (2) |
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277 | (8) |
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277 | (8) |
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10 Document Image Restoration and Analysis as Separation of Mixtures of Patterns: From Linear to Nonlinear Models |
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285 | (26) |
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285 | (4) |
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286 | (1) |
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10.1.2 Blind Source Separation Approach |
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287 | (1) |
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288 | (1) |
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10.2 Linear Instantaneous Data Model |
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289 | (7) |
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10.2.1 Single-Side Document Case |
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289 | (1) |
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10.2.2 Recto-Verso Document Case |
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290 | (1) |
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10.2.3 Solution through Independent Component Analysis |
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291 | (1) |
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10.2.4 Solution through Data Decorrelation |
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292 | (1) |
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10.2.5 Discussion of the Experimental Results |
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293 | (3) |
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10.3 Linear Convolutional Data Model |
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296 | (6) |
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10.3.1 Solution through Regularization |
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299 | (2) |
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10.3.2 Discussion of the Experimental Results |
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301 | (1) |
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10.4 Nonlinear Convolutional Data Model for the Recto-Verso Case |
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302 | (3) |
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10.4.1 Solution through Regularization |
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304 | (1) |
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10.4.2 Discussion of the Experimental Results |
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305 | (1) |
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10.5 Conclusions and Future Prospects |
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305 | (6) |
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307 | (4) |
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11 Correction of Spatially Varying Image and Video Motion Blur Using a Hybrid Camera |
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311 | (25) |
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311 | (2) |
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313 | (2) |
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11.2.1 Traditional Deblurring |
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313 | (1) |
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11.2.2 PSF Estimation and Priors |
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313 | (1) |
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11.2.3 Super Resolution and Upsampling |
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314 | (1) |
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11.3 Hybrid Camera System |
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315 | (4) |
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11.3.1 Camera Construction |
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316 | (1) |
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11.3.2 Blur Kernel Approximation Using Optical Flows |
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317 | (1) |
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11.3.3 Back-Projection Constraints |
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318 | (1) |
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11.4 Optimization Framework |
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319 | (6) |
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11.4.1 Richardson-Lucy Image Deconvolution |
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319 | (1) |
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11.4.2 Optimization for Global Kernels |
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320 | (1) |
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11.4.3 Spatially Varying Kernels |
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321 | (3) |
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324 | (1) |
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11.5 Deblurring of Moving Objects |
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325 | (1) |
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326 | (2) |
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11.7 Results and Comparisons |
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328 | (7) |
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335 | (1) |
Bibliography |
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336 | (5) |
Index |
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341 | |