On sparsity issues in compressive sensing based speech enhancement

Signal sparsity is the fundamental requirement of compressive sensing (CS) techniques. In our previous work, a CS-based speech enhancement algorithm has been proposed. However, several issues concerning speech sparsity have not yet been thoroughly studied. In this paper, we focus on studying the following issues: (1) the sparsity of clean speech and audio signals; (2) the sparsity of various noise signals; (3) analysis of the capacity of two sparse transforms i.e., wavelet and discrete cosine transform (DCT), to explore speech sparsity. In this respect, several measures are proposed to analytically compare the wavelet transform with DCT. We found that (1) signal compressibility is an important factor for the CS-based method. (2) DCT explores the best compressibility for noisy signals and achieves the best enhancement performance; (2) The CS-based speech enhancement methods are more efficient in reducing the noise with worse compressibility.