A compressive sensing method for noise reduction of speech and audio signals

Recently, compressive sensing (CS) has been intensively studied in the fields of applied mathematics and signal processing. However, its application to speech processing has not been well discussed. In this paper, we propose a compressive sensing method for noise reduction of speech and audio signals. The noise reduction problem is formulated in the theoretical framework of CS, as an ℓ₁-minimisation problem with a linear combination of a constrained term, by adopting a random partial Fourier transform operator. Furthermore, a gradient descend line search (GDLS) algorithm is adopted to efficiently solve the optimisation problem. Finally, we demonstrate that the proposed method is quite effective in reducing the noise of speech signals, especially for stationary and nonstationary white Gaussian noises.