Image denoising with two-dimensional zero attracting LMS algorithm

In this paper, we propose a new two-dimensional (2D) zero-attracting least-mean-square (ZALMS) adaptive filter by imposing a sparsity aware l1-norm penalty term into the cost function of the 2D-LMS algorithm. Comparisons with 2D-LMS and BM3D algorithms were conducted both on sparse and non-sparse images. The carried-out simulations show that the proposed algorithm has good capabilities in updating the filter coefficients along both horizontal and vertical directions, and its performance is similar with the 2D-LMS algorithm with lower computation time. But 2D-ZALMS performs better than BM3D algorithm.