| With the rapid development of 5G technology,artificial intelligence and wireless communication,a large number of sparse signal data is stored and transmitted in complex form.To reconstruct complex sparse signals,complex compressed sensing algorithm has become one of the key research contents.The existing algorithms for complex compressed sensing can be summarized as the first-order optimization algorithm for single variable complex compressed sensing.However,many signal data are often accompanied by block sparse features.For the signal data with block sparse features,designing efficient second-order complex compressed sensing block sparse algorithm is one of the research hot spots in recent years.Firstly,based on the compressed sensing technology and the characteristics of block sparse structure,we establish a new block sparse constraint optimization model.Furthermore,we analyze the properties of the objective function and the explicit expression of sparse constrained projection of this model.Then,with the help of the explicit expression,we define the optimality condition of the model: τ-stationary point and analyze the relationship between τ-stationary point and optimal solution,which obtains the first-order sufficient conditions and first-order necessary conditions of the model.Based on the above optimality conditions,we further develop a new efficient second-order algorithm: BNHTP algorithm and give the explicit expression for solving each sub-problem.In order to ensure that the BNHTP algorithm converges to the local minimum of the model,we use the above optimality condition as the stop condition of the BNHTP algorithm.Numerical experiments demonstrate that the BNHTP algorithm has superior performance in term of recovery accuracy and calculation time when compare with the AMP algorithm.In addition,the BNHTP algorithm also has better robustness to noisy data. |
