Provably secure and efficient audio compression based on compressive sensing

The advancement of systems with the capacity to compress audio signals and simultaneously secure is a highly attractive research subject. This is because of the need to enhance storage usage and speed up the transmission of data, as well as securing the transmission of sensitive signals over limited and insecure communication channels. Thus, many researchers have studied and produced different systems, either to compress or encrypt audio data using different algorithms and methods, all of which suffer from certain issues including high time consumption or complex calculations. This paper proposes a compressing sensing-based system that compresses audio signals and simultaneously provides an encryption system. The audio signal is segmented into small matrices of samples and then multiplied by a non-square sensing matrix generated by a Gaussian random generator. The reconstruction process is carried out by solving a linear system using the pseudoinverse of Moore-Penrose. The statistical analysis results obtaining from implementing different types and sizes of audio signals prove that the proposed system succeeds in compressing the audio signals with a ratio reaching 28% of real size and reconstructing the signal with a correlation metric between 0.98 and 0.99. It also scores very good results in the normalized mean square error (MSE), peak signal-to-noise ratio metrics (PSNR), and the structural similarity index (SSIM), as well as giving the signal a high level of security.