Reconstruction of sparse vectors in compressive sensing with multiple measurement vectors using bidirectional long short-term memory

In this paper we address the problem of compressive sensing with multiple measurement vectors. We propose a reconstruction algorithm which learns sparse structure inside each sparse vector and among sparse vectors. The learning is based on a cross entropy cost function. The model is the Bidirectional Long Short-Term Memory that is deep in time. All modifications are done at the decoder so that the encoder remains the general compressive sensing encoder, i.e., wide random matrix. Through numerical experiments on a real world dataset, we show that the proposed method outperforms the traditional greedy algorithm SOMP as well as a number of model based Bayesian methods including Multitask Compressive Sensing and Compressive Sensing with Temporally Correlated Sources. We emphasize that since the proposed method is a learning based method, its performance depends on the availability of training data. Nevertheless, in many applications huge dataset of offline training data is usually available.1