Abstract
Modeling helps simulate the behavior of a system for a variety of initial conditions, excitations and systems configurations, and that the quality and the degree of the approximation of the models are determined and validated against experimental measurements. Neural networks are very sophisticated techniques capable of modeling extremely complex systems employed in statistics, cognitive psychology and artificial intelligence. In particular, neural networks that emulate the central nervous system form an important part of theoretical and computational neuroscience. Further, since graphs are the abstract representation of the neural networks; graph analysis has been widely used in the study of neural networks. This approach has given rise to a new representation of neural networks, called Graph neural networks. In signal processing, wherein improving the quality of noisy signals and enhancing the performance of the captured signals are the main concerns, graph neural networks have been used quite effectively. Until recently, wavelet transform techniques had been used in signal processing problems. However, due to their limitations of orientation selectivity, wavelets fail to represent changing geometric features of the signal along edges effectively. A newly devised curvelet transform, on the contrary, exhibits good reconstruction of the edge data; it can be robustly used in signal processing involving higher dimensional signals. In this chapter, a generalized signal denoising technique is devised employing graph neural networks in combination with curvelet transform. The experimental results show that the proposed model produces better results adjudged in terms of performance indicators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Caundill, Neural networks primer part I. AI Expert 2(12), 46–52 (1987)
C.J. Stam, J. Reijneveld, Graph theoretical analysis of complex networks in brain. Nonlinear Biomed. Phys. 1(3), 215–223 (2007)
B. Bhosale, A. Biswas, Multi-resolution analysis of wavelet like soliton solution of KdV equation. Int. J. Appl. Phys. Math. 3(4), 270–274 (2013)
B. Bhosale et al., Wavelet based analysis in bio- informatics. Life Sci. J. 10(2), 853–859 (2013)
B. Bhosale et al., On wavelet based modeling of neural networks using graph theoretic approach. Life Sci. J. 10(2), 1509–1515 (2013)
B. Olshausen, D. Field, Emergence of simple-cell receptive filed properties by learning a sparse code for natural images. Nature 381, 607–609 (1996)
E. Candes, D. Donoho, Continuous curvelet transform: resolution of the wave front set. Appl. Comput. Anal. 19(2), 162–197 (2005)
N. Kota, G. Reddy, Fusion based gaussian noise removal in the images using curvelets and wavelets with gaussian filter. Int. J. Image Proc. 5(4), 230–238 (2011)
N. Yaser, J. Mahdi, A novel curvelet thresholding function for additive Gaussian noise removal. Int. J. Comput. Theory Eng. 3(4), 169–178 (2011)
R. Sivakumar, Denoising of computer tomography images using curvelet transform. ARPN J. Eng. Appl. Sci. 2(1), 26–34 (2007)
E. Hassan et al., Seismic signal classification using multi-layer perceptron neural network. Int. J. Comput. Appl. 79(15), 35–43 (2013)
Y. Shimshoni, N. Intrator, Classification of seismic signals by integrating ensembles of neural networks. IEEE Trans. Sig. Process. 46(5), 45–56 (1998)
A. Moya, K. Irikura, Inversion of a velocity model using artificial neural networks. Comput. Geosci. 36, 1474–1483 (2010)
E. Candes et al., Fast discrete curvelet transforms, multiscale modeling and simulation. Appl. Comput. Anal. 5(3), 861–899 (2006)
A. Weitzenfeld et al., The neural simulation language: a system for brain modeling (MIT Press, 2002)
F. Scarselli et al., The graph neural network model, neural networks. IEEE Trans. Syst. 20(1), 61–80 (2008)
I. Podolak, Functional graph model of a neural network. IEEE Trans. Syst. 28(6), 876–881 (1998)
X.U. Jim, B. Zheng, Neural networks and graph theory. Sci. China F 45(1), 1–24 (2002)
L. Badri, Development of neural networks for noise reduction. Int. Arab J Inf. Technol. 7(3), 156–165 (2010)
A. Hyvarinen, E. Oja, Independent component analysis: algorithms and applications. Neural Netw. 13(4–5), 411–430 (2000)
S. Shehata et al., Analysis of blind signal separation of mixed signals based on fast discrete curvelet transform. Int. Electr. Eng. J. 4(4), 1140–1146 (2013)
J.F. Cardoso, A. Souloumiac, Blind beam forming for non-gaussian signals. IEEE Proc. Part F 140(6), 362–370 (1993)
H. Valpola, Bayesian ensembel learning for non-linear factor analysis. Acta Ploytechnica Scand. Math. Comput. Ser. 108, 54–64 (2000)
M. Motwani et al., Survey of image denoising techniques, in Proceedings 2004 Global Signal Processing Expo and Conference (2004), pp. 27–30
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bhosale, B. (2016). Curvelet Interaction with Artificial Neural Networks. In: Shanmuganathan, S., Samarasinghe, S. (eds) Artificial Neural Network Modelling. Studies in Computational Intelligence, vol 628. Springer, Cham. https://doi.org/10.1007/978-3-319-28495-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-28495-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28493-4
Online ISBN: 978-3-319-28495-8
eBook Packages: EngineeringEngineering (R0)