Two-dimensional (2D) adaptive filtering is a technique that has been used for denoising in applications such as biomedical image processing in recent years. In this paper, we design the extension of the 1D-ARG adaptive filtering schemes to form new 2D-ARG adaptive filters. To compare the performance of the proposed algorithm in noise reduction in digital images, three images of different sizes from the Matlab library, Moon, Pout, and Cameraman, are taken as reference. This reduction is compared with two other gradient algorithms least mean squares (LMS) and normalized least mean squares (NLMS) for 2D adaptive filter design. Based on the simulation results and the established metrics, we demonstrate that the proposed method achieves a noise reduction eventually superior to the other 2D gradient algorithms.