创新点
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1.
构建了一个以“基元频率”为准则的稀疏信号主元分析方法。
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2.
“基元频率”准则适合于在非正交超完备空间(超完备字典)上的主元分析, 它也是稀疏信号的一个重要特征。
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3.
“稀疏信号主元分析”方法将信号的“能量集中特性”、“稀疏表达特性”和“基元高频率特性”集中于稀疏分解框架, 从而在抑制强噪声的同时有效地保留弱信号细节。
References
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Elad M, Aharon M. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process, 2006, 15: 3736–3745
Aharon M, Elad M, Bruckstein A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process, 2006, 54: 4311–4322
Zhao Q, Meng D Y, Xu Z B. Robust sparse principal component analysis. Sci China Inf Sci, 2014, 57: 092115
Deledalle C A, Denis L, Tupin F. Iterative weighted maximum likelihood denoising with probabilistic patch-based weights. IEEE Trans Image Process, 2009, 18: 2661–2672
Zhang Z, Li F, Zhao M, et al. Joint low-rank and sparse principal feature coding for enhanced robust representation and visual classification. IEEE Trans Image Process, 2016, 25: 2429–2443
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 60872131). The idea of the principal basis analysis presented here arises through a lot of deep discussions with Professor Henri Maître at Telecom-ParisTech in France. We are also grateful to Prof. Didier Le Ruyet at CNAM in France for many fruitful discussions.
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The authors declare that they have no conflict of interest.