Modeling neural networks and curvelet thresholding for denoising Gaussian noise

Abstract

Modeling facilitates simulating the behavior of a system for a variety of initial conditions, excitations and systems configurations. The quality and the degree of the approximation of the models are determined and validated against experimental measurements. Neural networks are very sophisticated modeling techniques capable of modeling extremely complex functions employed in statistics, cognitive psychology and artificial intelligence. Especially, neural network model that emulates the central nervous system is a part of theoretical as well as computational neuroscience. Since, graphs are the abstract representation of the neural networks, graph analysis has been used in the study of neural networks, anatomical and functional connectivity. This approach has given rise to a new representation of neural networks, called Graph neural network, which encompasses both Biological neural networks and Artificial neural networks. In machine learning and cognitive science, a class of artificial neural networks is a family of statistical learning algorithms inspired by biological neural networks (the central nervous systems of animals, in particular, the brain) and they are used to estimate or approximate functions that depend on a large number of unknown inputs. Particularly, in the area of signal processing, the prime goal of the neural networks is to obtain a good approximation for some input/output mapping, by enhancing the performance of captured signals. Consequently, improving quality of noisy signals/images through noise reduction has become an active area of research. In such noise reduction problems, the graph neural networks can be used quite effectively by suitably designing it to train with input sequences; which are assumed to be a composition of the desired signal plus an additive Random/Gaussian noise. Until recently, wavelets had been widely used in signal processing. However, wavelets suffer from the limitations of orientation selectivity and as a result, they fail to represent changing geometric features of the signal along edges effectively. Curvelet transform, on the contrary, exhibits good reconstruction of the edge data as it incorporates a directional component to the conventional wavelet transform and therefore can be robustly used in analysis of higher dimensional signals. In this paper, the endeavour is to employ graph neural networks in combination with the curvelet transform for the enhancement of the corrupted signal and device a unified signal denoising technique using appropriate thresholding function. The experimental results show that the proposed model produces better results in terms of signal to noise ratio and computed mean square error - the most commonly used measures to determine performance factor/quality of the captured signal.