Two dimensional zero-attracting variable step-size LMS algorithm for sparse system identification

In this paper, we introduce a two dimensional version of the zero-attracting variable step size LMS (ZA-VSSLMS) adaptive filter for image deconvolution. ZA-VSSLMS was proposed to improve the performance of the VSSLMS algorithm when the system is sparse. We design a new 2-D adaptive filter that not only updates its coefficients in both horizontal and vertical directions but more importantly improves the performance of the filter when the the point spread function (PSF) in an image deconvolution problem has a sparse structure. This is achieved by adding an ℓ₁ norm penalty function into the original cost function of the VSSLMS algorithm. The simulation results show improved PSNR compared to 2-D VSSLMS algorithm.