Distributed Compressive Sensing via LSTM-Aided Sparse Bayesian Learning

Model-driven algorithms on distributed compressive sensing with multiple measurement vectors (MMVs) have been generally based on the assumption that the vectors in the signal matrix are jointly sparse. However, the signal matrix in many practical scenarios violates the above assumption, since there might exist unknown dependency between vectors. It highlights the limitation of model-driven approaches and the necessity to move toward data-driven ones. In this paper, we propose a data-driven algorithm, which interprets the MMV problem as sequence modeling to infer the unknown dependency and encourage sparse signal recovery within the framework of sparse Bayesian learning (SBL). Specifically, we extend the fast-SBL algorithm suitable for MMV sparse recovery. Then the long short-term memory (LSTM) is introduced into the extended fast-SBL, serving as a strategy for selecting the basis function from the dictionary. Compared with existing data-driven algorithms, the proposed LSTM-SBL algorithm inheriting the characteristics of fast-SBL has fewer local minimums and better robustness to noise. Extensive experiments are conducted on MNIST and MSR datasets to evaluate the accuracy, robustness and speed of the LSTM-SBL algorithm. Experimental results are presented and analyzed to illustrate the potential advantages of the LSTM-SBL algorithm in contrast to state-of-the-art MMV recovery algorithms.