Fused Lasso Algorithm Based on Novel Non-Convex Regularization in Sparse Domain for Audio Signal Enhancement

In this paper, we present the fused lasso algorithm in the wavelet domain for audio signal enhancement in this research. The fused lasso algorithm gives more efficiency than other methods because this algorithm comprises two parts. The first part is called as the total variation method (TVM), and the second part is known as the penalized least squares regression (PLSR). The prominent point of the TVM is based on decreasing the pseudo-Gibbs phenomena. On the other hand, the PLSR with the convex condition, also called as the convex PLSR, gives the advantage in reducing noise. A lot of works study and develop the TVM; therefore, we focus on developing the convex PLSR in this work. In fact, the bias which is the gap between the estimated and noisy signals at the large magnitude of the noisy signal affects the performance of the convex PLSR. If this bias is small, also known as the small bias, then the convex PLSR gives better efficiency than other forms. Therefore, we present the novel non-convex regularization which can build the convex PLSR in the closed-form solution and the small bias. Here, the convex PLSR of the proposed regularization is presented not only in the closed-form solution and the small bias but also in the relationship to the group of wavelet coefficients, also called as the multivariate case. In the signal enhancement problem, experimental results show that the fused lasso algorithm and the convex PLSR based on the proposed regularization outperform state-of-the-art techniques in both the error of the l(2) norm (L2E) and visual quality.