sparse image representation via combined transforms - Convex ...

138 APPENDIX A. DIRECT EDGELET TRANSFORM
(a) Huo image
(b) Largest−200 coeff.
(c) Largest−400 coeff.
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20 40 60
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(d) Edgelet trans. coeff.(largest−10000/26752)
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0 5000 10000
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(e) Largest−800 coeff.
20 40 60
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(f) Largest−1600 coeff.
20 40 60
Figure A.1: Edgelet transform of the Chinese character “Huo”: (a) is the original; (d) is
the sorted coefficients; (b), (c), (e) and (f) are reconstructions based on the largest 200,
400, 800, 1600 coefficients, respectively.
The reason to do this is that both of them show some patchy patterns in the original images.
The filtered images show more obvious edge features. See Figure A.2 (b) and Figure A.4
(b).
A.3 Details
.
A direct way of computing edgelet coefficients is explained. It is direct in the sense that
every single edgelet coefficient is computed by a direct method; the coefficient is a weighted
sum of the pixel values (intensities) that the edgelet trespasses. For an N × N image, the
order of the complexity of the direct method is O(N 3 log N).
Section A.3.1 gives the definition of the direct edgelet transform. Section A.3.2 calculates
the cardinality of the edgelet system. Section A.3.3 specifies the ordering. Section A.3.4