修正的迭代近似梯度投影算法在压缩感知中的应用

Application of Modified Iteratively Approximated Gradient Projection Algorithm in Compressed Sensing

通过设计一种新的Hessian矩阵的近似,得到函数在当前迭代点的二次近似模型,并利用该模型与延迟策略得出一种新步长.结合新步长,提出一种求解压缩感知中稀疏信号重构问题的修正迭代近似梯度投影算法,并给出收敛性证明.实验结果表明,该算法不仅能较好地恢复原始信号中的非零元素,有效地重构信号,而且与经典算法相比,重构效率较高.

By designing a new approximation of Hessian matrix,we obtained a new quadratic approximate model of function in the current iteration point,and used this model and delay strategy to obtain a new stepsize.Combined with the new stepsize,we proposed a modified iteratively approximated gradient projection algorithm for solving the problem of sparse signal reconstruction in compressed sensing,and gave the proof of convergence.Experimental result shows that the proposed algorithm can not only restore the nonzero elements in the original signal,but also reconstruct the signal effectively.Compared with the classical algorithm,the proposed algorithm has higher reconstruction efficiency.