Image Restoration with Two-Dimensional Adaptive Filter Algorithms

Two-dimensional (2D) adaptive filtering is a technique that can be applied tomany image and signal processing applications. This paper extends the one-dimensionaladaptive 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-membershipNLMS (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 stepsizechanges during the adaptation which leads to improve the performance of thealgorithms. In 2D-SM adaptive filter algorithms, the filter coefficients are not updated ateach iteration. Therefore, the computational complexity is reduced. In 2D-SPU adaptivealgorithms, the filter coefficients are partially updated which reduce the computationalcomplexity. We demonstrate the good performance of the proposed algorithms thoroughseveral simulation results in 2D adaptive noise cancellation (2D-ANC) for imagedenoising. The results are compared with the classical 2D adaptive filters such as 2D-LMS,2D-NLMS, and 2D-APA.