Variable step-size compressed sensing-based sparsity adaptive matching pursuit algorithm for speech reconstruction

This paper presents a novel greedy reconstruction algorithm for speech signal, named the variable step-size sparsity adaptive matching pursuit algorithm (short for VSSAMP). As the name implies, this modified algorithm achieves an improvement compared with the state-of-the-art greedy algorithm sparsity adaptive matching pursuit (SAMP). The new algorithm varies the step size, which is fixed in SAMP. This innovation can accelerate the reconstruction speed and demonstrate a better performance on estimating the true signal´s support set to some extent. The step size is set to a large value initially so as to approach the real sparsity quickly. Afterwards, step size is cut down gradually and this mechanism is benefit for estimating the sparsity accurately. At the end of the novel method, a pruning step is utilized which can decrease the estimated sparsity one atom by one atom, based on reducing the reconstruction error. This step increases the accuracy of estimated sparsity and enhances the reconstruction performance. The comparisions of reconstruction performance and speed are exhibited in this paper. The simulation results show that the modified algorithm outperforms the SAMP algorithm when reconstructing absolutely sparse signals and speech signals.