Research Of Deep Leaning Method For Sparse Recovery With Multiple Measurements

As an extension of compressive sensing,multi-measurement compressive sensing has been applied in many areas of signal processing.This thesis mainly studies the deep-learning-based algorithm for sparse recovery with multiple measurements.The aim is to model the inter-signal dependency by applying the idea of “learning”,and to recover sparse signals from multiple measurements more accurately and efficiently.The thesis firstly introduces the background and state of the art of multi-measurement compressive sensing by classifying the existing algorithms and explaining the purpose of introducing deep learning.Then starting from the basis of sparse Bayesian learning(SBL),the thesis reviews the fundamental concepts and framework of Bayesian sparse recovery,including the hierarchal Bayesian model and the variational Bayes method.Based on the hierarchal Bayesian model,an efficient Bayesian sparse recovery algorithm is specifically introduced,i.e.fast-SBL,then the long-short time memory(LSTM)networks are applied on top of fast-SBL.By taking advantage of the LSTM's strong capability for sequential modelling,the study uses it to assist the basis selection process in fast-SBL,and proposes to combine SBL and LSTM for the first time,resulting in the LSTM-SBL algorithm.The thesis explains the framework and the theory of LSTM-SBL in detail,mainly focusing on its modelling for inter-signal dependencies and its improvement for fast-SBL.For training the LSTM network,the training data generation method and its training details are proposed.The experiments in the thesis are based on two real datasets,handwriting digit image and natural image.The two experiments are carried out to evaluate the performance of various multi-measurement sparse recovery algorithms,including their accuracy,speed and robustness.For the handwriting digit image recovery,the experiment shows LSTM-SBL can maintain high performance in high or medium SNR,and in low or medium sampling ratio.The NMSE decreases by 19%-48% compared to other algorithms in the experiment.For the natural image recovery,three categories of objects,i.e.flowers,buildings and bicycles,are selected in the experiment.The result shows LSTM-SBL outperforms other algorithms in all three categories,and this advantage maintains with varying number of signal source.