Intelligent Frequency Domain Image Filtering Based on a Multilayer Neural Network with Multi-Valued Neurons

Neural networks have shown significant promise in the field of image processing, particularly for tasks such as denoising and restoration, due to their capacity to model complex nonlinear relationships between inputs and outputs. In this study, we explored the application of a complex-valued neural network—a multilayer neural network with multi-valued neurons (MLMVN)—for filtering two types of noise in digital images: additive Gaussian noise and multiplicative speckle noise. The proposed approach involves processing images as a set of overlapping patches in the frequency domain using MLMVN. Training was performed using a batch learning algorithm, which proved to be more efficient for big learning sets: it results in fewer learning epochs and a better generalization capability. Experimental results demonstrated that MLMVN achieves noise filtering quality comparable to well-established methods, such as the BM3D, Lee, and Frost filters. These findings suggest that MLMVN offers a viable framework for image denoising, particularly in scenarios where frequency domain processing is advantageous. Also, complex-valued logistic and hyperbolic tangent activation functions were used for multi-valued neurons for the first time and have shown their efficiency.