sparse image representation via combined transforms - Convex ...

6 Simulations 119
6.1 Dictionary..................................... 119
6.2 Images . . ..................................... 120
6.3 Decomposition .................................. 121
6.4 Decay of Coefficients . .............................. 122
6.5 ComparisonwithMatchingPursuit....................... 125
6.6 Summary of Computational Experiments . .................. 127
6.7 Software...................................... 127
6.8 ScaleofEfforts .................................. 128
7 Future Work 129
7.1 Experiments . . . . . . .............................. 129
7.2 Modifying Edgelet Dictionary .......................... 131
7.3 Accelerating the Iterative Algorithm ...................... 131
A Direct Edgelet Transform 135
A.1 Introduction.................................... 135
A.2 Examples ..................................... 136
A.2.1 EdgeFilter ................................ 137
A.3 Details....................................... 138
A.3.1 Definition................................. 139
A.3.2 Cardinality ................................ 141
A.3.3 Ordering . . . .............................. 142
A.3.4 Computing a Single Edgelet Coefficient . . .............. 144
A.3.5 Adjoint of the Direct Edgelet Transform . . .............. 147
A.3.6 Discussion................................. 148
B Fast Edgelet-like Transform 149
B.1 Transformsfor2-DContinuousFunctions ................... 150
B.1.1 Fourier Slice Theorem .......................... 150
B.1.2 ContinuousRadonTransform...................... 151
B.2 Discrete Algorithm . . .............................. 152
B.2.1 Synopsis.................................. 153
B.2.2 Interpolation: from Discrete to Continuous Image .......... 153
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