Efficient measurement matrix for speech compressive sampling

Signal sampling is an important concern for compressive sensing framework. The use of efficient sampling may enhance the overall performance by collecting informative samples. The work done in this paper is aimed to propose the efficient sampling matrix for speech compressive sensing by reviewing the reconstruction results obtained via conventionally used measurement matrices. Recently used measurement matrices are either randomly structured or deterministic in nature. Therefore, the prime objective of this work is to analyse speed and reconstruction performance of l1-norm minimization algorithm when samples are provided by the concerned sampling matrix. The speed and accuracy analysis is intended to propose efficient sampling matrix which can facilitate faithful signal reconstruction process for speech compressive sensing. The sampling matrices chosen for this work are Bernoulli random matrix, Gaussian random matrix, Hadamard matrix and Toeplitz matrix. The observed matrices are carefully adjusted to provide different range of sampling ratios for signal recovery process. In this work, the number of input samples are changed (from 10% to 40%) to search for the efficient sampling matrix which can survive the least possible number of samples. The performances of the sampling matrices are compared on the basis of Root Mean Squared Error (RMSE) values and reconstruction time (in seconds) is obtained via l1 minimization method.