Block-sparsity Signals Recovery Via Recurrent Neural Network

Compressive sensing,which is a novel sampling paradigm that allows signals to be sampled with sub-Nyquist sampling rate,is one of the hottest research topics in signal processing over the last decades.The reconstruction algorithm of signals is priority among priorities,the quality of which concerns effects its applications in reality.Therefore,how to reduce the complexity and improve the precision of algorithms is the research emphasis in this field.We consider the problem of recovering block-sparse signals,whose nonzero elements occur in clusters.The recovery performance will naturally improve with utilization of block-sparse structure.However,the priori knowledge of block partitions is usually unavailable in practice.Conventional algorithms,led by Bayesian statistical approaches,are model-driven,which means the highest level they could attain is no more than the comprehension of researchers,even if these methods have achieved excellent results.Thus,we utilize the neural network,which has great power of information mining,in this work to improve the recovery performance.First of all,we sort out several categories of conventional algorithms and summarize their common shortcoming,that is,whether these models could indeed acquire the block structure.It is this common shortcoming that we propose our algorithm.On the other hand,the deep learning method has been applied to almost every research field as a powerful technology.In recent years,such thinking also appears in sparse coding.It provides a novel idea for the proposition.Among all sorts of models of deep learning,the recurrent neural network(RNN)has been proved to be very powerful in processing temporal signals with its excellent performance.We naturally extend its application to process spatial signals.Aimed at the dilemma of RNN in practical applications and the feature of block-sparsity recovery problem,we introduce the long short-term memory,which solves the inherent problem of RNN.Also,the idea of the best k-term approximation provides us a valuable lesson in this process.Besides,details of the proposed network,generation of training dataset and strategy of training this network are introduced as well.Finally,we compare the proposed algorithm with some state-of-the-art algorithms with different kinds of signals in several dimensionalities,including simulation signals,audio signals and image signals.The experimental results demonstrate the superiority of our proposed algorithm in both speed and precision.