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带边界条件约束的非相干字典学习方法及其稀疏表示

DOI: 10.16383/j.aas.2015.c140183, PP. 312-319

Keywords: 字典学习,非相干字典,等角紧框架,稀疏表示

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Abstract:

?从字典的相干性边界条件出发,提出一种基于极分解的非相干字典学习方法(Polardecompositionbasedincoherentdictionarylearning,PDIDL),该方法将字典以Frobenius范数逼近由矩阵极分解获取的紧框架,同时采用最小化所有原子对的内积平方和作为约束,以降低字典的相干性,并保持更新前后字典结构的整体相似特性.采用最速梯度下降法和子空间旋转实现非相干字典的学习和优化.最后将该方法应用于合成数据与实际语音数据的稀疏表示.实验结果表明,本文方法学习的字典能逼近等角紧框架(Equiangulartight-frame,ETF),实现最大化稀疏编码,在降低字典相干性的同时具有较低的稀疏表示误差.

References

[1]  Elad M, Aharon M. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 2006, 15(12): 3736-3745
[2]  Ramirez I, Sprechmann P, Sapiro G. Classification and clustering via dictionary learning with structured incoherence and shared features. In: Proceedings of the 23rd IEEE Conference on Computer Vision and Pattern Recognition (CVPR). San Francisco, CA: IEEE, 2010. 3501-3508
[3]  Candés E J, Eldar Y C, Needell D, Randall P. Compressed sensing with coherent and redundant dictionaries. Applied and Computational Harmonic Analysis, 2011, 31(1): 59-73
[4]  Duarte-Carvajalino J M, Sapiro G. Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Transactions on Image Processing, 2009, 18(7): 1395-1408
[5]  Zhang Q A, Li B X. Discriminative K-SVD for dictionary learning in face recognition. In: Proceedings of the 23rd IEEE Conference on Computer Vision and Pattern Recognition (CVPR). San Francisco, CA: IEEE, 2010. 2691-2698
[6]  Jiang Z L, Lin Z, Davis L S. Learning a discriminative dictionary for sparse coding via label consistent K-SVD. In: Proceedings of the 24th IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Washington D.C., USA: IEEE, 2011. 1697-1704
[7]  Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM Review, 2001, 43(1): 129-159
[8]  Donoho D L, Huo X M. Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 2001, 47(7): 2845-2862
[9]  Tropp J A. Greed is good: algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 2004, 50(10): 2231-2242
[10]  Donoho D L, Tsaig Y. Fast solution of l1-norm minimization problems when the solution may be sparse. IEEE Transactions on Information Theory, 2008, 54(11): 4789-812
[11]  Aharon M, Elad M, Bruckstein A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 2006, 54(11): 4311-4322
[12]  Mailhe B, Barchiesi D, Plumbley M D. INK-SVD: learning incoherent dictionaries for sparse representation. In: Proceedings of the 2012 International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Kyoto, Japan, USA: IEEE, 2012. 3573-3576
[13]  Barchiesi D, Plumbley M D. Learning incoherent dictionaries for sparse approximation using iterative projections and rotations. IEEE Transactions on Signal Processing, 2013, 61(8): 2055-2065
[14]  Yaghoobi M, Daudet L, Davies M E. Parametric dictionary design for sparse coding. IEEE Transactions on Signal Processing, 2009, 57(12): 4800-4810
[15]  Yaghoobi M, Daudet L, Davies M E. Structured and incoherent parametric dictionary design. In: Proceedings of the 2010 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Dallas, TX, USA: IEEE, 2010. 5486-5489
[16]  Cristian R. Design of incoherent frames via convex optimization. IEEE Signal Processing Letters, 2013, 20(7): 673-676
[17]  Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666
[18]  Elad M. Sparse and Redundant Representations: from Theory to Applications in Signal and Image Processing. New York: Springer, 2010. 95-100
[19]  Welch L. Lower bounds on the maximum cross correlation of signals. IEEE Transactions on Information Theory, 1974, 20(3): 397-399
[20]  Tropp J A, Dhillon I S, Heath R W, Strohmer T. Designing structured tight frames via an alternating projection method. IEEE Transactions on Information Theory, 2005, 51(1): 188-209
[21]  Horn R A, Johnson C R. Matrix Analysis. Cambridge, UK: Cambridge University Press, 1985. 411-427

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