Image Denoising with Two-Dimensional Adaptive Filter Algorithms

Two-dimensional (2D) adaptive filtering is a technique that can be applied to many image and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to 2D structure and the novel 2D adaptive filters are established. Based on this extension, the 2D variable step-size normalized least mean squares (2D-VSSNLMS), the 2D-VSS affine projection algorithms (2D-VSS-APA), the 2D set-membership NLMS (2D-SM-NLMS), the 2D-SM-APA, the 2D selective partial update NLMS (2DSPU-NLMS), and the 2D-SPU-APA are presented. In 2D-VSS adaptive filters, the stepsize changes during the adaptation which leads to improve the performance of the algorithms. In 2D-SM adaptive filter algorithms, the filter coefficients are not updated at each iteration. Therefore, the computational complexity is reduced. In 2D-SPU adaptive algorithms, the filter coefficients are partially updated which reduce the computational complexity. We demonstrate the good performance of the proposed algorithms thorough several simulation results in 2D adaptive noise cancellation (2D-ANC) for image denoising. The results are compared with the classical 2D adaptive filters such as 2D-LMS, 2D-NLMS, and 2D-APA.