Inversion-Free Sparse Bayesian Learning for Temporally Correlated Signal Recovery

Compressed sensing recovers the sparse signal from far fewer samples than required by the well-known Nyquist–Shannon sampling theorem to speed up the measure- ment procedure. The sparse signal recovery performance can be significantly improved by exploiting the temporal correlation in the multiple measurement vector model within the framework of sparse Bayesian learning. However, it is inevitable to involve the matrix inversion for existing methods, making the application of these schemes to large datasets impractical. To overcome this bottleneck, in this letter, we propose an inversion-free sparse Bayesian learning algorithm for temporally correlated sparse signal recovery, which is free of any matrix inversion operation and only requires simple addition and multiplication operations. Specifically, utilizing a property for the convex quadratic func- tion, we obtain a lower bound for the likelihood distribution that enables the computationally efficient model inference based on the expectation-maximization algorithm. Simulation results show its superior performance over other state-of-the-art methods in terms of the recovery performance and the running time.