15 April 2008 Ripplet transform for feature extraction
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Efficient representation of images usually leads to improvements in storage efficiency, computational complexity and performance of image processing algorithms. Efficient representation of images can be achieved by transforms. However, conventional transforms such as Fourier transform and wavelet transform suffer from discontinuities such as edges in images. To address this problem, we propose a new transform called ripplet transform. The ripplet transform is a higher dimensional generalization of the wavelet transform designed to represent images or two-dimensional signals at different scales and different directions. The ripplet transform is also a generalization of the curvelet transform. Specifically, the ripplet transform allows arbitrary support c and degree d while the curvelet transform is just a special case of the ripplet transform (Type I) with c = 1 and d = 2. Our experimental results show that the ripplet transform can provide efficient representation of images that contain edges. The ripplet transform holds great potential for image denoising and image compression.
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Jun Xu, Jun Xu, Dapeng Wu, Dapeng Wu, "Ripplet transform for feature extraction", Proc. SPIE 6970, Algorithms for Synthetic Aperture Radar Imagery XV, 69700X (15 April 2008); doi: 10.1117/12.777302; https://doi.org/10.1117/12.777302

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