2D-filter design based on Volterra equation and machine learning to tackle the aliasing effect in image demosicing

For nonlinear problems, the discrete Volterra equation is a helpful model. An aliasing effect between components from a CFA image is ‎known as the main problem in Demosaicing on frequency-domain analysis, which denotes a nonlinear problem. The discrete Volterra equa-‎tion can be used as a model to solve Demosaicing. A suitable Volterra kernel is required. We show that there is an analogy between the ‎weights and bias of the perceptron and the coefficients of the Volterra kernel. This analogy allows us to discover the coefficients of 2D-‎nonlinear filters by numerically solving the discrete Volterra equation. On the images from the Kodak database, this Demosaicing procedure ‎is applied in accordance with the Volterra equation's order and the Volterra kernel's size. Effectiveness is judged using several measures. ‎The study's findings show that the aliasing effect is lessened depending on the order of the Volterra equation and the Volterra kernel size ‎chosen. Our mean signal-to-noise ratio performance, using a 3x3 kernel size and the second-order Volterra equation, is 37.7 dB.