Compressive sensing-based speech enhancement in non-sparse noisy environments

In the authors previous work, a compressive sensing (CS)-based method has been proposed to address speech enhancement (SE) in adverse environments (CS-SPEN) based on an assumption of sparse noise. However, this assumption may not be satisfied in practical noisy environments. In this study, the authors study this issue by relaxing this assumption to consider a general non-sparse noise case, such that the proposed method naturally extends the previous one. In particular, they solve the theoretic difficulty of CS-SPEN on the treatment of non-sparse noise by using a relaxed upper bound for the constraint governing data consistency and a relaxed estimation error bound. Their main result is mathematically proved. In addition, the effectiveness of the proposed method is demonstrated by computational simulations, showing certain improvements to the previous method for both stationary and non-stationary white Gaussian noises across various segmental signal-noise-ratios (SNRs). In these cases, the proposed method is shown to have comparable results to the state-of-the-art SE alogrithms and some advantages over them at low SNRs. CS-SPEN without the sparse noise assumption works evenly with CS-SPEN with the sparse noise assumption for car internal and F16 cockpit noises.