Abstract
So far we have approached dictionary learning from the perspective of Chap. 2, where we are interested in the few nonzero entries of the representations. In literature this process is also called the synthesis-based sparse representation model. Recent years have shown approximation improvements when instead we analyze the set of atoms that do not participate in signal representation. If the sparse DL quest is to learn a dictionary able to identify the low-dimensional space that is the true origin of a given class of signals, in this new analysis-based cosparse representation model we are interested in finding its null-space complement. Throughout this chapter we look at representation and learning challenges posed by the cosparse domain and compare them to similar obstacles encountered by its sparse sibling.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Chatterjee, M. Vehkapera, M. Skoglund, Projection-based and look-ahead strategies for atom selection. IEEE Trans. Signal Process. 60(2), 634–647 (2012)
W. Dai, T. Xu, W. Wang, Simultaneous codeword optimization (SimCO) for dictionary update and learning. IEEE Trans. Signal Process. 60(12), 6340–6353 (2012)
J. Dong, W. Wang, W. Dai, Analysis SimCo: a new algorithm for analysis dictionary learning, in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, New York, 2014), pp. 7193–7197
M. Elad, P. Milanfar, R. Rubinstein, Analysis versus synthesis in signal priors. Inverse Prob. 23(3), 947 (2007)
R. Giryes, S. Nam, M. Elad, R. Gribonval, M. Davies, Greedy-like algorithms for the cosparse analysis model. Linear Algebra Appl. 441, 22–60 (2014)
P. Irofti, B. Dumitrescu, Overcomplete dictionary design: the impact of the sparse representation algorithm, in The 20th International Conference on Control Systems and Computer Science (2015), pp. 901–908
Q. Liang Q. Ye, Computing singular values of large matrices with an inverse-free preconditioned Krylov subspace method. Electron. Trans. Numer. Anal. 42, 197–221 (2014)
Z. Liu, J. Li, W. Li, P. Dai, A modified greedy analysis pursuit algorithm for the cosparse analysis model. Numer. Algorithms 74(3), 867–887 (2017)
S. Nam, M.E. Davies, M. Elad, R. Gribonval, The cosparse analysis model and algorithms. Appl. Comput. Harmon. Anal. 34(1), 30–56 (2013)
R. Rubinstein, A.M. Bruckstein, M. Elad, Dictionaries for sparse representations modeling. Proc. IEEE 98(6), 1045–1057 (2010)
R. Rubinstein, T. Peleg, M. Elad. Analysis K-SVD: a dictionary-learning algorithm for the analysis sparse model. IEEE Trans. Signal Process. 61(3), 661–677 (2013)
Y. Saad, Numerical Methods for Large Eigenvalue Problems, Revised edn. (SIAM, Providence, 2011)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Dumitrescu, B., Irofti, P. (2018). Cosparse Representations. In: Dictionary Learning Algorithms and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-78674-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-78674-2_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78673-5
Online ISBN: 978-3-319-78674-2
eBook Packages: EngineeringEngineering (R0)