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Learning Steerable Wavelet Frames

N. Chenouard, M. Unser

Proceedings of the Ninth International Workshop on Sampling Theory and Applications (SampTA'11), Singapore, Republic of Singapore, May 2-6, 2011.



We present a functional framework for the adaptive design of dictionaries where the invariance to translation, dilation, and rotation is built upfront into the primary representation space. Our key idea is to build an invariant signal representation prior to the learning stage. By doing so, we focus our effort on adapting the dictionary to the distinctive features of the signal, rather than to the cumbersome encoding of the desired invariance properties of the representation. We thus avoid the pitfall of traditional dictionary-learning techniques that need to allocate considerable computational power to laboriously obtain some degree of invariance of the representation space. Moreover, we avoid the redundancy of representation which is typical of early works on dictionary learning for image coding, where several translated, dilated, and rotated copies of the same two-dimensional function are necessary [4, 2, 1, 3], whereas we need just one.

References

  1. M. Aharon, M. Elad, A. Bruckstein, "K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation," IEEE Transactions on Signal Processing, vol. 54, no. 11, pp. 4311-4322, November 2006.

  2. M.S. Lewicki, B.A. Olshausen, "Probabilistic Framework for the Adaptation and Comparison of Image Codes," Journal of the Optical Society of America A: Optics and Image Science, and Vision, vol. 16, no. 7, pp. 1587-1601, July 1999.

  3. J. Mairal, G. Sapiro, M. Elad, "Learning Multiscale Sparse Representations for Image and Video Restoration," SIAM Multiscale Modeling and Simulation, vol. 7, no. 1, pp. 214-241, 2008.

  4. B.A. Olshausen, D.J. Field, "Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1?," Vision Research, vol. 37, no. 23, pp. 3311-3325, December 1997.


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