A novel sparse adaptive filter for suppressing impulsive disturbance in audio signals

Abstract

This work studies the sparse adaptive filter designs for audio signal recovery in the presence of impulsive disturbance. By exploiting the sparse representation of desired signal and compressibility of impulsive disturbance, a joint sparse least mean p-norm (JSLMP) optimization, in which ℓp-norm (1 ≤ p ≤ 2) measures the data fidelity and ℓq-norm (0 ≤ q ≤ 1) enforces sparse solutions, is developed, termed as ℓq-JSLMP. The filter weights update is derived using gradient descent, and the Adam and variable step size (VSS) are integrated to accelerate convergence and avoid potential local minima. For the special case of q = 1, namely ℓ1-JSLMP, its convergence condition and mean square deviation (MSD) analysis are derived. Finally, an application framework for processing corrupted audio signals is developed. Extensive experiments are conducted on both synthetic and real-measured impulsive noise data, comparing the proposed method with traditional algorithms as well as the deep learning-based GTCRN model. Results demonstrate that the proposed method yields superior perceptual quality and significantly lower memory consumption compared to GTCRN under impulsive disturbance.