Compressive sensing for perceptually correct reconstruction of music and speech signals

Compressive sensing (CS) is a technique that can achieve exact signal reconstruction by using fewer samples than those in the Nyquist theorem. In this study, listening tests were conducted to investigate the minimum number of samples needed for perceptually correct reconstruction by means of CS. The dictionary used as a sparsity domain for the signal reconstruction was the discrete cosine transform, and the reconstruction approach was the one provided by the L1-Magic. Three music signals and four speech signals were used as source signals. These signals were reconstructed by CS using different percentages of Nyquist samples. The results of the listening tests showed that, when 50% of the samples were used for the CS reconstruction, half of the test listeners judged the original and reconstructed signals to be perceptually the same. Listeners with musical training showed better sensitivity in distinguishing the original signals from the reconstructed signals than listeners without musical training. The log spectral distance between the original and reconstructed signals was a better objective index than the root mean square error and signal-to-noise ratio to evaluate the performance of the CS because inaccurate signal reconstruction mainly appeared at high frequencies. (C) 2021 Elsevier Ltd. All rights reserved.