Evaluation of Compressed Sensing and Recovery of Sound Signals Using Sparse Bayesian Learning Methods

Compressed sensing is a signal processing technique that is used for the efficient acquisition and reconstruction of signals by finding solutions to under-determined linear systems. In most cases, the compressed signal is recovered using the conventional $$l_{1}$$ norm minimization technique, which is a convex optimization procedure. However, the global minimum is not necessarily the sparsest solution. Therefore, another method called sparse Bayesian learning (SBL) is introduced for the reconstruction of compressed audio signals. Using the different SBL algorithms, a better reconstruction for the compressed audio signal is achieved. The SBL algorithm for the multiple measurement vector (MMV) model is also implemented for the audio signal. The results of different SBL techniques (SBL, T-SBL, MSBL, T-MSBL) are compared. We show via the experimental results that the time-varying model outperforms the other techniques. Further, we show that the T-MSBL algorithm reconstructed the original audio signal from the compressed signal more efficiently than the other algorithms.