Research On Multi-task Sparse Reconstruction Methods

Compressed sensing theory points out that the rate required for sampling compressible signals can be much lower than the Nyquist sampling rate,which brings a new perspective for signal sampling and processing.The design of sparse reconstruction algorithms to recover original signals from compressed sampling signals is one of the important research contents of compressed sensing.Compared with single-task reconstruction algorithms,multi-task sparse reconstruction can significantly reduce the number of compressed observations required for sparse signal reconstruction and improve the reconstruction performance of all tasks by taking advantage of the correlation between tasks.Combined with the structural characteristics of signals and the correlation between signals,this paper has investigated the multi-task sparse reconstruction algorithms based on matching pursuit,Bayesian estimation and variational Bayesian inference,and mainly completed the following work:Firstly,by extending the single-task orthogonal matching pursuit algorithm,this paper has designed a multi-task orthogonal matching pursuit algorithm(MT-OMP).This algorithm is simple and easy to implement,and it can improve the reconstruction performance by taking advantage of the same sparse signal support sets shared among tasks.A multi-task adaptive matching pursuit algorithm(MT-AMP)which can learn signal correlation between tasks has also been studied.This algorithm does not need to known the sparsity information in advance so it can be used in a wider range of application scenarios.Secondly,under the hierarchical Bayesian reconstruction model,this paper has carried out in-depth research on the multi-task sparse Bayesian reconstruction algorithm(MT-BCS)and its modified version(Modified MT-BCS).The two algorithms can realize precise inference of the posterior distribution by assuming the conjugate likelihood functions and prior distributions.Simulation experiments on the reconstruction of onedimensional and two-dimensional sparse signals show that more robust reconstruction performance can be achieved by sharing hyperparameters to learn correlations between tasks.Finally,in view of the problem that sparse signal support sets among multiple tasks may not be completely identical,a reconstruction model was designed to describe the block distribution of support sets among tasks.According to this model,a blockdistributed multi-task sparse reconstruction algorithm based on variational Bayesian inference(MT-BD-SSR)has been proposed.By introducing a hidden variable to indicate the different position of the support sets for different tasks,the information sharing is realized hyperparameters between tasks in a different’way.Through simulation experiments and comparative analysis,it is found that when the similarity of signal support sets among multiple tasks is not high,the reconstruction performance of MT-BDSSR algorithm is better than MT-BCS algorithm.