Stochastic optimization using automatic relevance determination prior model for Bayesian compressive sensing

Abstract

Compared with the conventional monitoring approach of separately sensing and then compressing the data, compressive sensing (CS) is a novel data acquisition framework whereby the compression is done during the sampling. If the original sensed signal would have been sufficiently sparse in terms of some orthogonal basis, the decompression can be done essentially perfectly up to some critical compression ratio. In structural health monitoring (SHM) systems for civil structures, novel data compression techniques such as CS are needed to reduce the cost of signal transfer and storage. In this article, Bayesian compressive sensing (BCS) is investigated for SHM signals. By explicitly quantifying the uncertainty in the signal reconstruction, the BCS technique exhibits an obvious benefit over the existing regularized norm-minimization CS. However, current BCS algorithms suffer from a robustness problem; sometimes the reconstruction errors are large. The source of the problem is that inversion of the compressed signal is a severely ill-posed problem that often leads to sub-optimal signal representations. To ensure the strong robustness of the signal reconstruction, even at a high compression ratio, an improved BCS algorithm is proposed which uses stochastic optimization for the automatic relevance determination approach to reconstructing the underlying signal. Numerical experiments are used as examples; the improved BCS algorithm demonstrates superior performance than state-of-the-art BCS reconstruction algorithms.