A Comparison Between Neural Network and Sampling Kantorovich Operators in Terms of Image denoising

Neural Network (NN) operators have gained significant attention in recent years due to their strong connections with Approximation Theory and their wide range of applications. In this paper, we investigate the potential of their multidimensional formulation, implementing an algorithm for digital image reconstruction. Specifically, we compare the performances of NN operators with those ones of the well-known sampling Kantorovich (SK) operators, whose implementation is a fairly recently used algorithm in image processing that serves as both a smoothing filter and a resolution enhancement tool. The comparison is conducted through a quantitative evaluation using three similarity indices: the Structural Similarity Index (SSIM), the Peak Signal-to-Noise Ratio (PSNR), and a newly introduced metric called Chemical structure diagram showing a hexagonal benzene ring with alternating double bonds. Attached to the benzene ring is a hydroxyl group (OH) and a carboxyl group (COOH). The structure represents an aromatic compound with functional groups.. A dataset of three reference images is used to assess the reconstruction quality of both approaches.