Zero-attracting LMS Algorithm Research Articles

Image denoising with two-dimensional zero attracting LMS algorithm

Image denoising with two-dimensional zero attracting LMS algorithm

Cauchy Distribution Function-Penalized LMS for Sparse System Identification

It is well known that the zero-attracting least mean square (ZA-LMS) algorithm and reweighted zero-attracting LMS (RZA-LMS) algorithm outperform the standard LMS algorithm in sparse systems. However, because the ZA-LMS algorithm does not distinguish the size of the tap coefficients, its performance in low-sparse or non-sparse systems declines rapidly. Although RZA-LMS selectively attracts taps with small magnitudes, there is extra attraction to large tap coefficients, which can increase the steady-state mean square error (MSE). In this paper, a Cauchy distribution function-penalized LMS (C-LMS) algorithm is proposed. The proposed algorithm changed the penalty term of the cost function into Cauchy distribution function, which can decrease the attraction to large tap coefficients and enhances the force to the small tap coefficients. The simulation results indicate that the C-LMS can achieve lower steady-state MSE than other algorithms in sparse systems and demonstrates similar performance to the conventional LMS algorithm in non-sparse system.

Robust Adaptive Algorithm by an Adaptive Zero Attractor Controller of ZA-LMS Algorithm

This paper proposes a new approach to identify time varying sparse systems. The proposed approach uses Zero-Attracting Least Mean Square (ZA-LMS) algorithm with an adaptive optimal zero attractor controller which can adapt dynamically to the sparseness level and provide appreciable performance in all environments ranging from sparse to nonsparse conditions. The optimal zero attractor controller is derived based on the criterion that confirms largest decrease in mean square deviation (MSD) error. A simple update rule is also proposed to change the zero attractor controller based on the level of sparsity. It is found that, for nonsparse system, the proposed approach converges to LMS (as ZA-LMS cannot outperform LMS when the system is nonsparse) and, for highly sparse system, as the proposed approach is based on optimal zero attractor controller, it converges either similar to ZA-LMS or even better than ZA-LMS (depending on the value of zero attractor controller chosen for ZA-LMS algorithm). The performance of the proposed algorithm is better than ZA-LMS and LMS when the system is semisparse. Simulations were performed to prove that the proposed algorithm is robust against variable sparsity level.