Sampling size in Monte Carlo Bayesian compressive sensing

Bayesian compressive sensing using Monte Carlo methods is able to handle non-linear, non-Gaussian signal models. The computational expense associated with Monte Carlo methods is, however, a concern especially in scenarios requiring real-time processing. In this work, a theoretical model is derived that provides insight on the relationship between performance and computational expense for a Monte Carlo Bayesian compressive sensing algorithm. The theoretical model is shown to accurately describe the practical performance of the algorithm. Additionally, the theoretical model is able to inexpensively project the algorithm's performance characteristics for various SNRs and computational complexity levels. The model is then useful in assessing the method's performance under different operational requirements.