Curvelet interaction with artificial neural networks

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.