Speech compressive sensing with ℓ1-minimzation and iteratively reweighted least squares-ℓp-minimization: A comparative study

The interests in Compressed Sensing (CS) come from its ability to provide sampling as well as compression, enhancement, along with encryption of the source information simultaneously. All these advantages have made CS, researched and applied in numerous speech-processing applications. In this paper, we compare ℓ1-minimization and Iteratively Reweighted Least Squares (IRLS)-ℓp-minimization algorithms to reconstruct speech signal from compressive observations. Using random Gaussian matrix, Compressive Sensing is performed on Discrete Cosine Transform (DCT) coefficients to evaluate the performance of algorithms based on Perceptual Evaluation Speech Quality measure (PESQ) and computational complexity for different compression ratios. Results revealed that IRLS-ℓ p-minimization provided modest advantage in reconstructed speech quality and proved to be faster than ℓ1-minimization for high compression ratios; in contrary to the case of lower compression ratios (lower than 40%).